Question and Answer

Question 06

Answer 06

Question 07

Answer 07

Question 08

Answer 08

Question 09

Answer 09

Question 10

Answer 10

Question 11

How many months have 30 day.

Answer 12

Cubic units.

Question 13

Answer 13

Question 14

Solve 2log₃(x) = 5

Answer 14

2log₃(x) = 5
Since 243 = 3⁵, we can replace 5 with log₃(243)

Therefore 2 log₃(x) = log₃(243)
⇒ log₃(x²) = log₃(243)
⇒ x² = 243
⇒ x = √(243) = 9√(3)

ALTERNATIVELY:
2log₃(x) = 5
⇒ log₃(x) = 2.5
⇒ As an exponent: 3^2.5 = x
⇒ x = 3²3^0.5 = 9√(3)

Question 15

Which of the following is not irrational?

(a) (3 + √7)

(b) (3 – √7)

(d) 3√7

Answer 15

(c) (3 + √7) (3 – √7)

Explanation: If we solve, (3 + √7) (3 – √7), we get;

(3 + √7) (3 – √7) = 3²– (√7)² = 9 – 7 = 2 [By a²– b² = (a – b) (a + b)]

Question 16

Answer 16

Question 17

When training for the Olympics, Ben Beacon's longest jump was 28 ft 6 in. In the finals of the Olympics he won with a jump that was 8 inches longer. How long was Ben's longest jump during the Olympics?

A 336 inches

B 340 inches

C 342 inches

D 350 inches

Answer 17

28 feet = 28 × 12 inches = 336 inches
So in training, he jumped 28 ft 6 inches = 336 inches + 6 inches = 342 inches.

In the Olympics he jumped 8 inches further.

342 inches + 8 inches = 350 inches

Question 18

A Car Is Traveling 75 Kilometers Per Hour. How Many Meters Does The Car Travel In One Minute?

Answer 18

1250 Meters/Minute

Question 19

The percentage of 1:4 is:

A. 75%

B. 50%

C. 25%

D. 100%

Answer 19

Explanation: 1:4 = 1/4

(1×100)/(4×100) = 1/4 x 100% = 0.25 x 100% = 25%

Question 20

The solution of 2x-3=7 is:

A. 5

B. 7

C. 12

D. 11

Answer 20

Explanation: 2x-3=7

2x=7+3=10

x=10/2 = 5

Question 21

Solve the equation

3x - 4 = 4 - (8 + 3x)

(A) 7

(B) 0

Answer 21

3x - 4 = 4 - (8 + 3x)

3x - 4 = 4 - 8 - 3x

3x + 3x = -4 + 4

6x = 0

x = 0/6

x = 0

Question 22

A father is 30 years older than his son, and one year ago he was four times as old as his son. Find the father’s present ages.

Answer 22

Let x be the son's age

Father's age = x + 30

One year ago,

Age of father = x + 30 - 1 ==> x + 29

Son's age = x - 1

x + 29 = 4(x - 1)

x + 29 = 4x - 4

3x = 33

x = 11

Age of son = 11 years

Age of father = 30 + 11 ==> 41 years

Question 23

What is the value of (-8) × (+4) ?

Answer 23

(-8) × +4 = -32

Question 24

The largest number which divides 70 and 125, leaving remainders 5 and 8, respectively, is

(A) 13

(B) 65

(D) 1750

Answer 24

Since 5 and 8 are the remainders of 70 and 125, respectively. Thus after subtracting these remainders from the numbers, we have the numbers

65 = (70 − 5), 117 = (125 − 8) which is divisible by the required number.

Now required number = H.C.F of (65,117)

$jagran josh$

Question 25

For some integer m, every odd integer is of the form

(A) m

(B) m + 1

(D) 2m + 1

Answer 25

As the number 2m will always be even, so if we add 1 to it then, the number will always be odd.

Question 26

Write The Place Value Of 7 In The Given Number Is 57368.

Answer 26

7000

Question 27

The square root of 0.0081 is ………… .

A. 0.09
B. 0.9
C. 0.91
D. 0.009

Answer 27

0.09

Question 28

Sky planted 3 trees in 9 minutes. How long did it take to plant each tree?

A 6

B 3

C 4

D 27

Answer 28

Planting 3 in 9 minutes is:

9 / 3 = 3 minutes per tree

(Using the multiplication fact: 3 × 3 = 9)

Question 29

Andy read 4/5 th of a story book which has 100 pages. How many pages of the book is not yet read by Andy?

A. 40
B. 60
C. 80
D. 20

Answer 29

D. 20

Question 30

Solve 5y = 20 using known multiplication facts.

Answer 30

5y means 5 × y
5 × 4 = 20, so y = 4

Question 31

If tomorrow is Wednesday, what day is it today?

Sunday

Tuesday

Monday

Thursday

Answer 31

Tuesday

Question 32

What is the amplitude for the function y = 3.2cos(1.5t + 6π)?

A 1.5

B 3.2

C 4.8

D 6

Answer 32

Generally for y = Acos(Bt + C) + D the amplitude is |A|
In this case, a = 3.2
So, the amplitude = |3.2| = 3.2

Question 33

What is the square root of 70.56?

A 8.4

B 8.5

C 8.6

D 9.4

Answer 33

To find the square root of 70.56, we need to know what number when multiplied by itself gives the answer 70.56

8² = 64 (less than 70.56)
9² = 81 (more than 70.56)

So the answer must be between 8 and 9.

Let's try 8.5

8.5 × 8.5 = 72.25 which is more than 70.56

Let's try 8.4

8.4 × 8.4 = 70.56 exactly

So √70.56 = 8.4

Question 34

There are 2,000 liters of water in a water tank.

It then rains heavily for 7 hours, adding 90 liters of water to the tank each hour.
How much water is there in the tank after 7 hours?

Answer 34

The total amount of water added= 7 × 90 liters = 630 liters
So the amount of water in the tank after 7 hours = 2,000 liters + 630 liters = 2,630 liters

Question 35

ABC is a triangle with A = (4, 5), B = (5, -1) and C = (-7, 4)

Without drawing the triangle, decide which one of the following most accurately describes ABC:

A A right-angled triangle

B An isosceles triangle

C An equilateral triangle

D A scalene triangle

Answer 35

Step 1 Find the slopes of sides of the triangle and compare them:

$[cached] 0.047922134399414 ms$

Step 2 Find the lengths of sides of the triangle and compare them:

$[cached] 0.025033950805664 ms$

Question 36

If you subtract a smaller odd number from a larger even number, the answer is:?

Answer 36

Even - Odd = Odd
For example, 10 - 7 = 3

Question 37

Solve |2x - 3| ≤ 7, giving your answer in interval notation.

Answer 37

|2x - 3| ≤ 7
⇒ -7 ≤ 2x - 3 ≤ 7

Add 3:
-7 + 3 ≤ 2x - 3 + 3 ≤ 7 + 3
⇒ -4 ≤ 2x ≤ 10

Divide by 2:
-4/2 ≤ 2x/2 ≤ 10/2
-2 ≤ x ≤ 5

As an interval this can be written as: [-2, 5]

Question 38

Sam took 4 minutes to cut a board into 2 pieces.
How long would it take Sam to cut a similar board into 3 pieces?

Answer 38

8 minutes

It only takes ONE cut to make 2 pieces
And TWO cuts to make 3 pieces.

So it simply takes twice as long.

Question 39

Roger has 7 stick lollies, Sylvia has 10 stick lollies and Tom has 16 stick lollies. They put all their lollies together and then share them equally among the three of them. How many stick lollies do they each get?

Answer 39

The total number of lollies is found by adding:
7 + 10 + 16 = 33

Now divide the total by 3 to see how many they get each:
33 ÷ 3 = 11
So they get 11 lollies each.

8 minutes

Question 40

Klara and Zosia had 60 matches altogether. Klara took as many matches as she needed to build a triangle, each side 6 matches long. Zosia used the remaining matches to build a rectangle, which had one side equal to 6 matches. How many matches long is each of the longer sides of this rectangle?

Answer 40

Klara needed 3 × 6 matches = 18 matches

60 - 18 = 42

That left Zosia with 42 matches to build the rectangle; so the perimeter of the rectangle was 42
⇒ The length + the breadth of the rectangle = 21

So if one side of the rectangle is 6 matches long, the other side must be 15 matches long.

Question 41

Chris rode 2,050 miles to win the Tour de France cycle race. How many yards is that?

Answer 41

1 mile = 1,760 yards

So 2,050 miles = 2,050 × 1,760 yards = 3,608,000 yards

Question 42

What are the Cartesian coordinates of the point C?

Answer 42

The point C is 6 squares to the right of the origin and 3 squares up from the origin.
Therefore it has x coordinate 6 and y coordinate 3.
Therefore it is (6, 3)

Question 43

Which integer on the number line is 8 more than -3?

Answer 43

To find 8 more than -3:
Start at -3 and move 8 places to the right, which is +5

Question 44

There are several angles in the diagram. Which angle is the smallest?

Answer 44

The smallest angle is this one:

This angle has vertex O and arms OD and OE.
The middle letter is where the angle actually is (its vertex), which is O.

Therefore we could write the angle as ∠DOE or ∠EOD

Question 45

A triangle has angles in the ratio 7 : 11 : 18
What is the size of the middle one of the three angles?

Answer 45

7 + 11 + 18 = 36
So we have to divide 180° into 36 equal parts:
180° ÷ 36 = 5°

The middle angle is 11 parts = 11 × 5° = 55°

Question 46

A dress originally cost $120.
In a Sale, the dress was sold with 12½% off the original price.
What was the sale price?

Answer 46

Amount deducted in the Sale = 12½% of $120 $[cached] 0.020027160644531 ms$

Amount deducted in the Sale = 12½% of $120
$[cached] 0.020027160644531 ms$

So the Sale price = $120 − $15 = $105

Question 47

Write p × p × p × p × p × p × p × p × p in exponent form.

Answer 47

The exponent of a number says how many times to use the number in a multiplication.
In this case the number p is used nine times, so the exponent is 9.

So, p × p × p × p × p × p × p × p × = p⁹

^{Question 48}

^{Convert 0.503 % to a decimal}

^Answer 48

^{To convert from a percent to a decimal, divide by 100 (and remove the "%" sign).
The easiest way to divide by 100 is to move the decimal point 2 places to the left
So 0.503 % = 0.00503}

^{Question 49}

^{It is estimated that the median house price in the US has increased by 16 times in the last fifty years.
What is this as a percent?}

^Answer 49

^{To convert from a decimal to a percent, multiply by 100 (and add a "%" sign).
The easiest way to multiply by 100 is to move the decimal point 2 places to the right
So 16 = 16.00 = 1600%}

^{Question 50}

Simplify 9⁵ ÷ 9^-3

Answer 50

Use the law of exponents x^m ÷ xⁿ = x^{m − n}
In this case m = 5 and n = -3 ⇒ m − n = 5 − (-3) = 5 + 3 = 8
So 9⁵ ÷ 9^-3 = 9⁸

^{Question 51}

^{What is (7 + 3) ÷ (8 − 3) ?}

^{Answer 51}

^{Work out the brackets (parentheses) first:
7 + 3 = 10
8 − 3 = 5
Therefore (7 + 3) ÷ (8 − 3) = 10 ÷ 5 = 2}

^{Question 52}

^{Multiply 3.25 by 0.22}

^{Answer 52}

^{Start with: 3.25 × 0.22}^{Multiply without decimal points: 325 × 22 = 7,150

3.25 has 2 decimal places,
and 0.22 has 2 decimal places,
so the answer has 4 decimal places: 0.7150

The final zero is not necessary, so: 0.715}

^{Question 53}

^{Which one of the following is not an integer?}

^{Answer 53}

^{The set of integers includes all whole numbers, their negatives and zero.
Integers = {..., -5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5, ...}

√2 = 1.414..., therefore, is not an integer.}

^{Question 54}

^{The diagram shows two adjacent sides of a regular polygon. What is the name of the polygon?}

^{Answer 54}

Method 1:
The total of all Exterior Angles is 360°, and 360°/40° = 9

So it is a 9-sided polygon, or nonagon.

Method 2:
The Exterior Angle is 40°, so the Interior Angle is (180° − 40°) = 140°
If one interior angle of the polygon is 140°, and n is the number of sides, then
(n − 2) × 180°/n = 140°
⇒ 180(n − 2) = 140n
⇒ 180n − 360 = 140n
⇒ 180n − 140n = 360
⇒ 40n = 360
⇒ n = 360/40 = 9

So it is a 9-sided polygon, or nonagon

^{Question 55}

What value of x makes the sentence x + 8 = 11 true?

^{Answer 55}

3 + 8 = 11 is true.
So, x = 3

^{Question 56}

Add the decimal numbers 2.7 and 4.1

^{Answer 56}

Put the decimals one under the other, keeping the decimal points in line. Add just like you would add whole numbers:
2.7+4.1=6.8

^{Question 57}

Divide (4x² − 6x) by 2x

^{Answer 57}

$[cached] 0.048160552978516 ms$

^{Question 58}

What is 219,376 rounded to the nearest 1,000?

^{Answer 58}

The digit in the hundreds place (3) is less than 5, so the 9 (in the thousands place) is rounded down to 9.

So 219,378 rounded to the nearest 1,000 is 219,000

^{Question 59}

How many minutes are there between half past nine and ten o'clock?

^{Answer 59}

Between half past nine and ten o'clock is half an hour.
$[cached] 0.046014785766602 ms$

^{Question 60}

An ant walks around a circle which has a radius of 20 cm.
How far has the ant walked?

^{Answer 60}

Answer to the nearest centimeter.

Use the formula C = 2 × π × r

Distance walked = Circumference = 2 × π × 20 cm

= 125.66... cm

= 126 cm to the nearest cm

^{Question 61}

What is the area of the largest circle that can be drawn inside a rectangle of sides 14 cm and 18 cm?

Use (22/7) as an approximation for π

^{Answer 61}

A rectangle of sides 14 cm and 18 cm can accommodate a circle of maximum diameter 14 cm.

If the diameter is 14 cm, then the radius is 7 cm.

So the area of the largest circle, A is given by

$[cached] 0.043869018554688 ms$

And so the area of the largest circle would be 154 cm²

^{Question 62}

^{How many acute angles are there in this pentagram?}

^{Answer 62}

^{Each of the five triangles at the points of the pentagram has three acute angles.
So there are 5 × 3 = 15 acute angles altogether in the pentagram.
(All other angles are not acute)}

^{Question 63}

Kyle started with 9,000 coins and gave away 1,000 every day until he had 4,000 left.
How many days did that take?

^{Answer 63}

Kyle started with 9,000
After 1 day he had 8,000
After 2 days he had 7,000
After 3 days he had 6,000
After 4 days he had 5,000
After 5 days he had 4,000

So it took 5 days.

^{Question 64}

Alex rounded 151 to the nearest ten. What result did she get?

^{Answer 64}

The last digit is less than 5, so we round the 5 down
And so, 151 rounded to the nearest ten is 150

^{Question 65}

Diana has three twelfths of a cake, Ed has two twelfths and Fergus has five twelfths. Grace has the rest.
How many twelfths does Grace have?

^{Answer 65}

First find the total of Diana, Ed and Fergus' shares:
$[cached] 0.052928924560547 ms$

Altogether one whole cake is equal to twelve twelfths.
$[cached] 0.020980834960938 ms$

^{Question 66}

Simplify the following expression by combining like terms:

-8x + 11y − 2y + 7x

^{Answer 66}

They are not all like terms.
However, -8x and 7x are like terms, so can be simplified:
-8x + 7x = -1x = -x
Similarly, 11y and -2y are like terms, so can be simplified:
11y − 2y = 9y

Therefore
-8x + 11y − 2y + 7x = -x + 9y

^{Question 67}

Solve x + 4 = 10 using known addition facts.

^{Answer 67}

6 + 4 = 10, so x = 6

^{Question 68}

What is the perimeter of this shape?

[image]

^{Answer 68}

Remember to add all the numbers shown.
3 + 3 + 3 + 3 + 3 + 3
Six 3s are 18

^{Question 69}

How long is the pencil according to the ruler? [image]

^{Answer 69}

"cm" means centimeters.

The pencil starts at 2 cm, and ends at the 11 cm mark.

11 - 2 = 9

So it is 9 cm long.

^{Question 70}

5 − 4 + 3 − 2 + 1 = ?

^{Answer 70}

Method 1
Work from left to right:

(5 − 4) + 3 − 2 + 1 ⇒ 1 + 3 − 2 + 1

(1 + 3) − 2 + 1 ⇒ 4 − 2 + 1

(4 − 2) + 1 ⇒ 2 + 1

(2 + 1) ⇒ 3

Method 2
Change the order of the additions and subtractions:

5 − 4 + 3 − 2 + 1
= 5 + 3 + 1 − 4 − 2
= 9 − 6
= 3

^{Question 71}

I have 16 lollipops.
One quarter of them are green, and one third of the rest are orange.
How many lollipops are not green or orange?

^{Answer 71}

^{16 ÷ 4 = 4 are green
That leaves 16 − 4 = 12 that are not green.
12 ÷ 3 = 4 are orange.
That leaves 12 − 4 = 8 that are neither green nor orange.}

^{Question 72}

^{Solve x + 4 = 10 using known addition facts.}

^{Answer 72}

^{6 + 4 = 10, so x = 6}

^{How many months have 30 day.}

^{Answer 73}

^{4 months}

^{Question 74}

^{What is 0.5 + 1.18?}

^{Answer 74}

^1.68

^{Question 75}

^{What is 1.23m + 63cm?}

^{Answer 75}

The answer is 1.86m

Convert the cm into metres and you will have 1.23 + 0.63 giving 1.86m

Question 76

solve for x

12x – 17 = 151

Answer 76

x = 14:

12(14) – 17 = 168 – 17 = 151

Question 77

There are 15 runners in a race and a fifth of them wear red.
How many runners wear red?

Answer 77

"A fifth" means to divide by 5

[image]
This shows 15 runners and a fifth of them wear red.
3 of them wear red.
(It doesn't matter what colors the other runners wear)

Or, using division:
15 ÷ 5 = 3

Question 78

If 12c - 2(c + 1) = 8c + 22, then the value of 'c' is...

Answer 78

12c - 2(c + 1) = 8c + 22
=> 12c - 2c - 2 = 8c + 22
=> 12c - 2c - 8c = 22 + 2
=> 2c = 24
=> c = 24/2
=> c = 12

Question 79

Convert the decimal number 123.375 to a hexadecimal number.

Answer 79

Consider the whole number part and the decimal part separately:

Whole number:
123 = 112 + 11 = (7 × 16) + 11
And 11 in hexadecimal is B
Therefore as a hexadecimal number 123 is 7B

Decimal:
$[cached] 0.052928924560547 ms$
Therefore as a hexadecimal number .375 is .6

So, 123.375 in decimal = 7B.6 in hexadecimal.

Question 80

x-2=2

Answer 80

x-2=2

x=2+2

x=4

Question 81

What is 28.1972 rounded to the nearest 0.01?

Answer 81

The digit in the thousandths place (7) is greater than or equal to 5, so the 9 (in the hundredths place) is rounded up to 10

So 28.1972 rounded to the nearest 0.01 is 28.20

Question 82

Simon has a bookcase with 6 shelves.
Each shelf contains 67 books.

How many books does Simon have altogether?

Answer 82

67 × 6 = 402

Question 83

For subtraction of time, what is 10:11 − 6:49 ?

Answer 83

Follow these steps:
* Subtract the hours
* Subtract the minutes
* If the minutes are negative, add 60 to the minutes and subtract 1 from hours.

Subtract the Hours: 10 − 6 = 4
Subtract the Minutes: 11 − 49 = -38
The minutes are less than 0, so add 60 to Minutes (-38 + 60 = 60 − 38 = 22 Minutes) and subtract 1 from Hours (4 − 1 = 3 Hours) ... answer is 3:22

Question 84

What is ((-3, 6) ∩ (0, 3)) ∪ (-2, 1) in interval notation?

Answer 84

[image]

(-3, 6) ∩ (0, 3) = (0, 3)
So ((-3, 6) ∩ (0, 3)) ∪ (-2, 1) = (0, 3) ∪ (-2, 1) = (-2, 3)

Question 85

Estimate the square root of 53.82 to one decimal place.

Answer 85

7 × 7 = 49
8 × 8 = 64

53.82 is closer to 49 than 64, so the square root of 53.82 will be closer to 7 than 8

Try 7.1:
7.1 × 7.1 = 50.41 - close, but maybe we can get closer.

Try 7.2:
7.2 × 7.2 = 51.84 - closer.

Try 7.3:
7.3 × 7.3 = 53.29 - very close.

Try 7.4:
7.4 × 7.4 = 54.76 - worse again.

53.82 is closer to 53.29 than it is to 51.84 or 54.76, so 7.3 is as close as we can get to √53.82 using only one decimal place.

Question 86

What is the cube root of 2197?

Answer 86

Question 87

Rs.1200 divided among P, Q and R. P gets half of the total amount received by Q and R. Q gets one-third of the total amount received by P and R. Find the amount received by R?

Answer 87

Explanation:

Let the amounts to be received by P, Q and R be p, q and r.
p + q + r = 1200
p = 1/2 (q + r) => 2p = q + r
Adding 'p' both sides, 3p = p + q + r = 1200
=> p = Rs.400
q = 1/3 (p + r) => 3q = p + r
Adding 'q' both sides, 4q = p + q + r = 1200
=> q = Rs.300
r = 1200 - (p + q) => r = Rs.500.

Question 88

Write the following statement in the form of an equation:The sum of three times x and 10 is 13.

Answer 88

3x + 10 = 13

Question 89

Answer 89

The total number of lollies is found by adding:
7 + 10 + 16 = 33

Now divide the total by 3 to see how many they get each:
33 ÷ 3 = 11
So they get 11 lollies each.

Question 90

What is [(40 − 5) ÷ (8 − 3) + 2] × 6

Answer 90

Work out the round brackets (parentheses) first:
40 − 5 = 35
8 − 3 = 5
Therefore (40 − 5) ÷ (8 − 3) = 35 ÷ 5 = 7
Next add the 2
⇒ (40 − 5) ÷ (8 − 3) + 2 = 7 + 2 = 9
Now we've worked out what's inside the square brackets (parentheses), we multiply by 6:
9 × 6 = 54

Question 91

A bag contains equal number of Rs.5, Rs.2 and Re.1 coins. If the total amount in the bag is Rs.1152, find the number of coins of each kind?

Answer 91

Let the number of coins of each kind be x.
=> 5x + 2x + 1x = 1152
=> 8x = 1152 => x = 144

Question 92

What number has a 5:1 ratio to the number 10?

Answer 92

Explanation:

5:1 = x: 10

x = 50

Question 93

A man is four times as old as his son. 10 years later, the man will be three times as old as his son. What is the man’s current age?

Answer 93

Question 94

The sum of the squares of three numbers is 138, while the sum of their products taken two at a time is 131. Their sum is:

Answer 94

Let the numbers be a, b and C. Then,

a² + b² + c² = 138 and (ab + bc + ca) = 131

(a + b + c)² = a² + b² + c² + 2(ab + bc + ca)

138 + 2 * 131 = 400

(a + b + c) = √400 = 20

Question 95

The ratio between two numbers is 3:4 and their sum is 420. The greater of the two numbers is:

A. 175
B. 200
C. 240
D. 315

Answer 95

Answer: Option C

Explanation:

The numbers be 3x and 4x

=> 3x + 4x = 420

=> 7x = 420

=> x = 60

Greater number = 4 Ã— 60 = 240

Question 96

A number exceeds 20 % of itself by 40. The number is:

A. 50
B. 60
C. 80
D. 320

Answer 96

Answer: Option A

Explanation:

Number be x.

=> X “ (20/100) x = 40

or 5 x “ x = 200

or x = 50

Question 99

John has three times as many marbles as Ken and Ken has four times as many marbles as Lewis.
Lewis has five marbles, so how many more marbles does John have than Lewis?

Answer 99

Lewis has 5 marbles
Ken has four times as many marbles as Lewis, so Ken has 4 × 5 = 20 marbles
John has three times as many marbles as Ken, so John has 3 × 20 = 60 marbles

Therefore Lewis has 5 marbles and John has 60 marbles
60 - 5 = 55
John has 55 more marbles than Lewis.

Question 100

I have 6 lollipops, one third of them are orange.
How many lollipops are not orange?

Answer 100

"A third" means to divide by 3

[image]

This shows 6 lollipops and one third of them are orange.
2 of them are orange
So, 4 of them are not orange.
(It doesn't matter what colors the other lollipops are)

Or, using division and subtraction:
6 ÷ 3 = 2 and 6 − 2 = 4

Question 101

How many odd numbers are in this list?
2, 10, 4, 6, 3, 8, 9, -1

Answer 101

2, 10, 4, 6 and 8 are even.
3, 9 and -1 are odd.

So there are 3 odd numbers.

Question 102

A daughter is 3 years old, and her mother is 28 years older than the daughter. How many years later will the mother be three times older than her daughter?

Answer 102

The mother's present age = 28 + 3 = 31

In 11 years' time,
the daughter will be 3 + 11 = 14 years old
and the mother will be 31 + 11 = 42 years old

3 × 14 = 42
So the mother will be three times older than her daughter in 11 years' time

Question 103

Naomi works for 8 hours each day for 5 days a week and 50 weeks in a year.
How many hours does Naomi work altogether in one year?

Answer 103

8 hours each day for 5 days a week for 50 weeks in a year
= (8 × 5 × 50) hours
= (40 × 50) hours

4 × 5 = 20
So (40 × 50) hours = 2,000 hours

Question 104

Marco rounded 496.41 to the nearest hundred. What result did he get?

Answer 104

The digit in the 'tens' place is 9, which is greater than or equal to 5, so we round the 4 in the 'hundreds' place up to a 5.

And so, 496.41 rounded to the nearest hundred is 500
(496.41 gets "rounded up" to 500)

Question 105

George had 162 different rocks and lost 26. How many rocks are left?

Answer 105

Take 26 from 162 and the answer is 136

Question 106

Simplify: a¹³ × a⁹ ÷ (a³)⁵

^{Answer 106}

First use the law (x^m)ⁿ = x^mn to simplify (a³)⁵:
(a³)⁵ = a^{3 × 5} = a¹⁵

Therefore a¹³ × a⁹ ÷ (a³)⁵ = a¹³ × a⁹ ÷ a¹⁵

Now use the law x^m × xⁿ = x^{m + n} to simplify the first two terms:
Therefore a¹³ × a⁹ ÷ a¹⁵ = a^{13 + 9} ÷ a¹⁵ = a²² ÷ a¹⁵

Finally use the law x^m ÷ xⁿ = x^{m - n} to complete the simplification:
Therefore a²² ÷ a¹⁵ = a^{22 − 15} = a⁷

Putting it all together:
a¹³ × a⁹ ÷ (a³)⁵
= a¹³ × a⁹ ÷ a¹⁵
= a²² ÷ a¹⁵
= a⁷

Question 107

^{Subtract the following decimal fractions:}

Answer 107

^{The denominators are the same, so just subtract the numerators:}

^{Question 108}

^{What is the least common multiple of 28 and 32?}

^{Answer 108}

^{The multiples of 28 are: 28, 56, 84, 112, 140, 168, 196, 224, 252, ...
The multiples of 32 are: 32, 64, 96, 128, 160, 192, 224, 256, ...

Therefore, the least common multiple of 28 and 32 is 224.}

^{Question 109}

^{Tania deposited $1,500 into a bank account that paid a simple interest rate of 2% per year.
How much interest had she earned after 9 years?}

^{Answer 109}

^{Question 110}

^{In a number with at least two digits, the last digit was deleted. The resulting number was n times smaller than the previous one.
Which is the greatest possible value of n?}

^{Answer 110}

^{Suppose the number has 3 digits and is of the form 100a + 10b + c where 1 ≤ a ≤ 9, 0 ≤ b ≤ 9 and 0 ≤ c ≤ 9
When the ones digit is deleted, the new 2-digit number is 10a + b

Let's try n = 20
⇒ 100a + 10b + c = 20(10a + b)
⇒ c = 100a + 10b
This has no solutions for the possible values of a, b and c.

Let's try n = 19
⇒ 100a + 10b + c = 19(10a + b)
⇒ c = 90a + 9b
This has solution a = 0, b = 1 and c = 9.
So the number is in fact a 2-digit number = 19.
Check When the ones digit is deleted, we get the new number, 1 ;and our original number, 19, is also 19 × our new number. So it works.

The greatest possible value of n, therefore, is 19.}

^{Question 112}

The L-shape A′B′C′D′E′F′ is the image of the L-shape ABCDEF after reflection in which of the following lines?

^{Answer 112}

Each point and its image must be the same distance from the mirror line, which is x + y = 7

Question 113

Find the acute angle θ that satisfies csc(θ) = 1.25

Answer 113

Cosecant is the reciprocal of Sine.

$[cached] 0.031948089599609 ms$

Question 114

In the picture DC = AC = 1 and CB = CE = 4.
The area of triangle ABC is equal to S.
What is the area of the quadrilateral AFDC?

Answer 114

In triangle ABC,
½ × 1 × 4 × SinC = S
⇒ 2SinC = S
⇒ SinC = ½S

Area of triangle DCA = ½ × 1 × 1 × SinC = ¼S

Area of triangle BCE = ½ × 4 × 4 × SinC = 4S

Let the area of quadrilateral AFDC be T.
⇒ Area of triangle DFA = T - ¼S

Triangles BFE and DFA are similar with scale factor 4 ⇒ The area factor = 4² = 16

⇒ Area of triangle BFE = 16 × Area of triangle DFA = 16(T - ¼S) = 16T - 4S

But
Area of triangle BCE = Area of triangle BFE + Area of triangle ABC + Area of triangle DCE - Area of quadrilateral AFDC
⇒ 4S = 16T - 4S + S + S - T
⇒ 15T = 6S
$[cached] 0.025033950805664 ms$

Question 115

Solve for a.

p=w/a

Answer 115

a = w/p

Question 116

Amy has three siblings - Ben, Cindy and Dai.
Ben is five years older than Amy
Cindy is twice as old as Amy.
Dai is seven years less than three times Amy's age.
The sum of all their ages is 19.
How old is Amy?

Answer 116

Let Amy's age be y years.

Ben is five years older than Amy ⇒ Ben's age is (y + 5) years.
Cindy is twice as old as Amy ⇒ Cindy's age is 2y years.
Dai is seven years less than three times Amy's age ⇒ Dai's age is (3y − 7) years.
The sum of all their ages is 19
⇒ y + (y + 5) + 2y + (3y − 7) = 19
Remove the parentheses :
⇒ y + y + 5 + 2y + 3y − 7 = 19
Collect together like terms :
⇒ y + y + 2y + 3y + 5 − 7 = 19
⇒ 7y − 2 = 19
Add 2 to both sides :
⇒ 7y − 2 + 2 = 19 + 2
⇒ 7y = 21
Divide both sides by 7
⇒ 7y/7 = 21/7
⇒ y = 3
Therefore Amy is 3 years old.

Question 117

The next day after his birthday Jas said: "The day after tomorrow will be Thursday." On what day of the week did Jas have his birthday?

Answer 117

When Jas said "The day after tomorrow will be Thursday." it must have been Tuesday.

This was the next day after his birthday, so his birthday was on Monday.

Question 118

What is the perimeter of sector AOB?

Use π = 3.14

Answer 118

The perimeter consists of a curved part (which is the arc AB) and two straight parts.

$[cached] 0.08702278137207 ms$

The two straight parts are both radii of the circle, so the length of each straight part = 10 cm

Therefore, the perimeter of sector AOB = 9.42 cm + 2 × 10 cm = 29.42 cm

Question 119

Eric has 51 balloons and Ernie has 45 balloons.
Eric has how many more balloons than Ernie?

Answer 119

To find how many more balloons Eric has, we just need to subtract:
51 − 45 = 6

Question 120

What is the least common multiple of 32 and 36?

Answer 120

The multiples of 32 are: 32, 64, 96, 128, 160, 192, 224, 256, 288, 320, ...
The multiples of 36 are: 36, 72, 108, 144, 180, 216, 252, 288, 324, ...

Therefore, the least common multiple of 32 and 36 is 288.

Question 121

Which one of the following IS a factor of 819?

Answer 121

819
= 3 × 273
= 3 × 3 × 91
= 3 × 3 × 7 × 13

3, 7 and 13 are all prime numbers, so the prime factors of 819 are 3, 3, 7 and 13.

Therefore, 91 (= 7 × 13) is a factor of 819,
but 93 (= 3 × 31), 95 (= 5 × 19) and 97 are not factors of 819.

Question 122

Shawn the builder estimated that it would cost $12,000 to build a new conservatory.
In fact it cost $13,200

What was the percentage error?

Answer 122

Use the formula:
$[cached] 0.036001205444336 ms$

Substitute Approximate Value = $12,000 and Exact Value = $13,200

$[cached] 0.048160552978516 ms$

Question 123

The Harmonic Mean of two numbers is 8

One of the numbers is 20. What is the other number?

Answer 123

Let the other number be x

There are three steps to finding the Harmonic Mean:

Step 1 Calculate the reciprocal for every value:
$[cached] 0.074148178100586 ms$

Step 2 Find the mean of those reciprocals:
$[cached] 0.040054321289062 ms$

Step 3 Then find the reciprocal of that mean:
$[cached] 0.082015991210938 ms$

$[cached] 0.030040740966797 ms$

So, the other number is 5

Question 124

CAN YOU WORK OUT THE SOLUTION TO THIS PROBLEM?

11 x ( 2 + 2 ) = ?

Answer 124

11 x 4 = 44

Question 125

If we minus 712 from 1500, how much do we get?

Answer 125

788

Question 126

What does PEMDAS stand for?

Answer 126

Parenthesis Exponents Multiplication Division Addition Subtraction.

Question 127

Simplify : 3 + 6 x (5 + 4) ÷ 3 - 7

Answer 127

Question 128

How many months are there in twelve years?

Answer 128

144

Question 129

Geoff thinks of a number. He deducts five from it and then divides the result by three. His answer is 25. What number did he start with?

Answer 129

Question 130

Which of the following pairs are Twin Primes?

Answer 130

Twin Primes are a pair of prime numbers that differ by 2 (successive odd numbers that are both prime numbers).

9 = 3 × 3, so is not prime. So (7, 9) are not Twin Primes.
49 = 7 × 7, so is not prime. So (47, 49) are not Twin Primes.
77 = 7 × 11, so is not prime. So (77, 79) are not Twin Primes.
107 and 109 are both prime numbers, so they are Twin Primes

The only pair of Twin primes is (107, 109).

Question 131

What is the least common multiple of 12, 24, 30, and 60?

Answer 131

120

Question 132

I have 16 lollipops.
One quarter of them are green, and one third of the rest are orange.
How many lollipops are not green or orange?

Answer 132

"One quarter" means to divide by 4 and "one third" means to divide by 3.

[image]

This shows 16 lollipops.
One quarter of them are green. Four are green.
That leaves 12 lollipos that are not green:
[image]

Of the rest, one third are orange. Four are orange.
That leaves 8 of them that are of different colors.
(It doesn't matter what colors the other lollipops are)

Or, using division:
16 ÷ 4 = 4 are green
That leaves 16 − 4 = 12 that are not green.
12 ÷ 3 = 4 are orange.
That leaves 12 − 4 = 8 that are neither green nor orange

Question 133

4 * 2 - 10 + 3 * 3 = ?

Answer 133

Question 134

Find x=?, when: 2x + 8 = 4x - 4

Answer 134

Question 135

35 ÷ ? = 7

Answer 135

Question 136

What is the value of (-10) × (-4)² × (+3) ?

Answer 136

Do this in three steps, working out (-4)² first:

1. (-4)² = (-4) × (-4)
Remember that multiplying two negative numbers makes a positive number
So (-4) × (-4) = +16
We now have (-10) × (+16) × (+3)

2. Work out (-10) × (+16)
Remember that multiplying a negative number by a positive number makes a negative number.
So (-10) × (+16) = -160

3. Work out (-160) × (+3)
Remember that multiplying a negative number by a positive number makes a negative number.
So (-160) × (+3) = -480

So the answer is -480

Question 137

What value of y makes the sentence 18 − y = 2 × y true?

Answer 137

18 − 6 = 12 and 2 × 6 = 12, so
18 − 6 = 2 × 6
So, y = 6

Question 138

How many even numbers are in this list?

14, 2, 5, 9, 24, 11, 28, 20, 18, 29

Answer 138

14, 2, 24, 28, 20 and 18 are even.
5, 9, 11 and 29 are odd.

So there are 6 even numbers.

Question 141

Jill planted 8 trees in 72 minutes. How long did it take to plant each tree?

Answer 141

Planting 8 in 72 minutes is:

72 / 8 = 9 minutes per tree

(Using the multiplication facts: 9 × 8 = 72 or 8 × 9 = 72)

Question 142

Simplify √160
by making the number inside the square root as small as possible (but still a whole number).

Answer 142

√160 = √(16 × 10) = √16 × √10 = 4√10

Note that 2√40 is not the simplest form.

Question 143

Ken borrowed $8,500 for 8 years at 3½% simple interest rate.
How much interest is that?

Answer 143

Use I = Prt
where
I = Interest
P = Principal = $8,500
r = interest rate = 3½% = 0.035
t = time = 8 years
Therefore I = $8,500 × 0.035 × 8 = $2,380

Question 144

AB and CD are parallel lines and EH is a transversal.
The size of angle EFB is 3x° and the size of angle DGH is x°

What is the value of x?

Answer 144

Angles EFB and FGD are corresponding angles, so are equal

Also, ∠FGD = 3x°

Angles FGD and DGH are adjacent angles on a straight lines, so add to 180°

⇒ 3x° + x° = 180°
⇒ 4x = 180
⇒ x = 45

Question 145

If you had 48 chocolates, a friend gave you 3 more, then another friend gave you 3 more,
how many chocolates would you have altogether?

Answer 145

You started with 48.
After your first friend gave you 3, you would have 51.
After another friend gave you 3, you would have 54.

Question 146

Henry started with 63 balloons and added 3 more every week until he had 78 altogether.

How many weeks did that take?

Answer 146

Henry started with 63.
After 1 week he had 66.
After 2 weeks he had 69.
After 3 weeks he had 72.
After 4 weeks he had 75.
After 5 weeks he had 78.

So it took 5 weeks.

Question 147

Given that 35 × 2 = 70, what is the value of 34 + 36?

Answer 147

35 × 2 is the same as 35 + 35.

34 is 1 less than 35, and 36 is 1 more than 35.

So, 34 + 36 is exactly the same as = 35 + 35 = 70.

Question 149

How many minutes are there between two o'clock and three o'clock?

Answer 149

Between two o'clock and three o'clock is one hour.
One hour is equal to 60 minutes.

Question 150

Ida is four inches shorter than Jeremy.

If we know how tall Ida is, how would we calculate Jeremy's height?

Answer 150

Ida is four inches shorter than Jeremy, so Jeremy must be four inches taller than Ida.

Therefore, we add 4.

Question 157

What is a prime number?

Answer 157

A number that is only divisible by itself or 1

Question 158

For the equation 3x + 4 = 12

+ is

Answer 158

Symbols such as +, −, ×, ÷, etc are called operators, so + is an operator.

Question 159

For the equation (3t − 1) ÷ 10 = 5

÷ is

Answer 159

Symbols such as +, −, ×, ÷, etc are called operators, so ÷ is an operator.

Question 160

The two triangles are similar.
What is the ratio of the sides of the left triangle to the corresponding sides of the right triangle?

Answer 160

2 : 3 = 3 : 4.5 = 3.5 : 5.25

So the ratio of corresponding sides is 2 : 3

Question 162

How many minutes from 12:35 to 1:40

Answer 162

From 12:35 to 1:35 is one hour, or 60 minutes.
PLUS another 5 minutes would make 1:40.

So 65 minutes total.

Question 164

What is the value of (+7) × (-6) ?

Answer 164

Remember that multiplying a positive number by a negative number makes a negative number.
So, (+7) × (-6) = -42

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