Quant question with answers

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Quant question with answers

1) What percent of 20 is 16?

A 3.2%
B 16%
C 36%
D 80%
E 125%

2)Organisers of a trade fair projected an increase of 20% in the number of visitors over the previous year, but the number of visitors actually increased by 50%. By what percentage was the actual number of visitors greater than the projected number of visitors?

A 20%
B 25%
C 30%
D 50%
E 125%

4)In 1997, flower sales on St Valentines Day were 6% of the total for the year. If flower sales on that day were $7,200,000 then what were the total flower sales for the whole year?

A $ 432,000
B $ 1,200,000
C $ 43,200,000
D $ 120,000,000
E $ 2,628,000,000

5) It costs $1.75 to buy a loaf of white bread and $2.00 to buy a loaf of wholemeal bread. Jenny buys 10 loaves of bread and the total cost is $18.50. How many wholemeal loaves did she buy?

A 4
B 5
C 6
D 7
E 8

7) A plank of wood is 24 feet long and is cut into 3 pieces. The longest piece is 3 feet longer than either of the other 2 pieces. How many feet long is the longest piece?

A 15
B 14
C 13
D 10
E 7

6) Paul is now 8 years older than Quill. 17 years ago Paul was twice as old as Quill. How old will Quill be in 10 years?

A 43
B 35
C 33
D 27
E 25

8) In a group of people solicited by charity 25% contribute $20, 45% contributed $10 and the rest contributed $5. If the charity received a total of $750 from those who contributed $5, how much did they receive in total from those solicited?

A $5,500
B $5,250
C $4,750
D $2,500
E $1,700

9)
A car costs d dollars a day to hire and an additional m dollars for evey 100 miles travelled. How much would it cost to hire the car for 7 days if you travel a total of 500 miles?

A 3500dm
B 5(7d + m)
C 7d + 500m
D 7d + 5m
E 7d +

10) What is the value of x, if

2(2x + 1) = 8(x - 3)

A -4
B -1
C 4
D 8
E 10

12)The function * is defined so that

a * b = a(b - a)
Which of the following expressions has the value 6?

A 1 * 6
B 2 * 3
C 2 * 4
D 3 * 5
E 5 * 3

6) Write out in the form of equations where P and Q represent the ages of Paul and Quill now.

'Paul is now 8 years older than Quill.'
P = Q + 8

'17 years ago Paul was twice as old as Quill.'
P - 17 = 2(Q - 17)

'How old will Quill be in 10 years?'
Q + 10 = ?
Next solve the equations.
P - 17 = 2(Q - 17) We know that P = Q + 8 so we can replace the P in the second equation with Q + 8.
Q + 8 - 17 = 2(Q - 17) Simplify both sides.
Q - 9 = 2Q - 34 Add 34 and take Q from both sides of the equation.
25 = Q NB: This is not the answer, we were asked to find Q + 10 so add 10 to both sides of the equation.
35 = Q + 10

Quill will be 35 in 10 years time and the answer is B.

 

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ANSWERS

1) Explanation


You can avoid any confusion in this question by doing a simple translation of the sentence into a mathematical expression.

In these cases, 'of' translates to 'times', 'is' to 'equal to' and 'what' to an unknown.

of -- ×
is -- =
Translating 'what percent of 20 is 16?', becomes,
?% × 20 = 16

?% =

?% =
You should remember that = 80%, therefore the correct answer is D.

Answers

2) Explanation

The actual number of visitors was 150% of last year and the projected number was 120%.

% = = = = 125%
The actual number fo visitors was 125% of those projected, therefore it was 25% greater.

B is the correct answer.

Answers


3) Explanation

On the second night the biologist founnd that 6 of the 30 foxes caught had already been tagged. This is or of those caught. This suggests that the first night the 30 foxes they had tagged constituted of the population.

Therefore the best estimate for the fox population is 5 × 30 = 150.

The answer is D.

Answers

4) Explanation

$7,200,000 is 6% of the total sales. Writing this as an equation we get

$7,200,000 = 6% × total sales
Therefore
total sales = $7,200,000 ÷ 6%

total sales = $7,200,000 ÷

total sales = $7,200,000 ×

total sales = $1,200,000 × 100

total sales = $120,000,000

So, the best answer is D

Answers

5) Explanation

If Jenny had bought 10 loaves of wholemeal it would have cost $20.00 in total. Since 10 × $2.00 = $20.00.

Jenny only spent $18.50 and therefore spent $1.50 less. Each white loaf is $0.25 less than each wholemeal loaf. Therefore she bought 6 white loaves since 6 × $0.25 = $1.50

Therefore the other 4 loaves must have been wholemeal and the correct answer is A.

Answers

11) In country X income tax is calculated in the following way. No tax is levied on the first $6,000 dollars earned each year and 25c tax is levied on every dollar over $6,000. Bob earned y dollars last year, if y is greater than $6,000 then how much should Bob pay?

A y
B 1,500 + y
C (y - 6,000)
D (6,000 - y)
E (6,000 + y)

Answers

7) Explanation

Let us say that the longest piece of wood has lenght L. The the 2 shorter peices both have length L - 3. So

L + (L-3) + (L-3) = 24 Simplify the left hand side.
3L - 6 = 24 Add 6 to both sides.
3L = 30 Divide by 3.
L = 10

The longest piece is 10 feet long. The answer is D.

Answers

8) Explanation

Put the information into a table.

% of those solicited amount given (each) amount given (total)
25% $20
45% $10
$5 $750

We will need to add a 'number of people' column.

% of those solicited amount given (each) amount given (total) number of people
25% $20
45% $10
$5 $750

Next we can work out the percentage who contributed $5.
% who contributed $5 = %100 - %25 - %45 = %30
And the number of people who contributed $5
number of people who contributed $5 = = 150
Add this new information into the table.

% of those solicited amount given (each) amount given (total) number of people
25% $20
45% $10
30% $5 $750 150

30% of those solicited is 150 people then, 25% is 125 people and 45% is 225 people. Add into the table.

% of those solicited amount given (each) amount given (total) number of people
25% $20 125
45% $10 225
30% $5 $750 150

From this we can work out how much money was contributed by each group of people.

125 people contributed $20 which is, 125 × $20 = $2500
225 people contributed $10 which is, 225 × $10 = $2250

% of those solicited amount given (each) amount given (total) number of people
25% $20 $2500 125
45% $10 $2250 225
30% $5 $750 150

To find the total we just add the amount contributed by each group.

Total = $2250 + $2500 + $750 = $5500
Therefore, answer A is correct

Answers

9) Explanation

The cost of hiring the car for 7 days at d dollars per day is

7d
The additional cost of travelling 500 mile at m dollars per 100 miles is
× m = 5m
Therfore the total cost for hiring the car for 7 days and travelling 500 miles is
7d + 5m
The correct answer is D.

Answers

10) Explanation

It is difficult to work with exponents if their bases are different as is the case in this question where the bases are 2 and 8 respectively. But there is a relationship between these two numbers that we can use to help us solve the equation.

23 = 8
If we use this to replace 8 in the original equation we get.

2(2x + 1) = 8(x - 3) Replace 8 by 23.
2(2x + 1) = (23)(x - 3) To calculate the exponent of an exponent multiply the two exponents.
2(2x + 1) = 2(3x - 9) We can eliminate the bases now because they are equal.
2x + 1 = 3x - 9 Subtract 2x from both sides.
1 = x - 9 Add 9 to both sides.
10 = x

Therefore, E is the correct answer.

Answers


11)

Explanation

Remember Bob does not pay any tax on the first $6,000 he earned. Therefore he only pays tax on the amount over $6,000 which can be expressed as

y - 6,000
He pays 25c per dollar on this amount which is
(y - 6,000) = (y - 6,000)
Therefore the correct answer is C.

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12) Explanation

The only way to do this question is to evaluate each expression in turn.

1 * 6 = 1 × (6 - 1) = 1 × 5 = 5
2 * 3 = 2 × (3 - 2) = 2 × 1 = 2
2 * 4 = 2 × (4 - 2) = 2 × 2= 4
3 * 5 = 3 × (5 - 3) = 3 × 2 = 6 Correct.
5 * 3 = 5 × (3 - 5) = 5 × -2 = -10

3 * 5 = 6 and so D is correct.