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Question September 23rd, 2008

Quantitative Set-1
Here are someGre quantitative aptitude question.



1) What percent of 20 is 16?

A 3.2%

B 16%

C 36%

D 80%

E 125%

3) Biologists working to estimate the population of foxes in small town captured and tagged 30 foxes on one night. The
foxes were then released. The next night they captured 30 foxes and found that 6 of them had already been tagged. The
best estimate for the fox population of the town would be
A 30

B 36

C 60

D 150

E 180

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

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 +

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

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)

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

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.

10) What is the value of x, if
2(2x + 1) = 8(x - 3)
A -4

B -1

C 4

D 8

E 10

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


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

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

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


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.

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.

Answers



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.
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Last edited by kartik; September 25th, 2008 at 09:56 PM..
   
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Re: Quantitative Set-1 Question with answers
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Re: Quantitative Set-1 Question with answers - June 29th, 2015

1)The difference of the squares of two consecutive even integers is divisible by which of the following numbers?

A. 3

B. 6

C. 4

D. 7

2) Which one of the following numbers is completely divisible by 99?

A. 115909

B. 115919

C. 115939

D. 115929

3) How many terms are there in the G.P. 4, 8, 16, 32, ... , 1024?

A. 9

B. 8

C. 7

D. 6


ANSWERS

1) Answer : Option C

Explanation :

---------------------------------------------------
Solution 1
---------------------------------------------------
Let the consecutive even integers are n and (n + 2)

difference of the squares = (n + 2)2 - n2 = (n2 + 4n + 4) - n2 = 4n + 4 = 4(n + 1)

which is divisible by 4

---------------------------------------------------
Solution 2 (preferred way)
---------------------------------------------------
Just take any of the two consecutive even integers say 2 and 4

difference of the squares = 42 - 22 = 16 - 4 = 12 which is divisible by 4


2) Answer : Option D

Explanation :

If a number is divisible by two co-prime numbers, then the number is divisible by their

product also.

If a number is divisible by more than two pairwise co-prime numbers,

then the number is divisible by their product also.

Read more

If a number is divisible by another number, then it is also divisible by all the factors

of that number.

Read more

We know that 99 = 9 × 11 where 9 and 11 are co-prime numbers. Also 9 and 11 are

factors of 99. Hence

if a number is divisible by 9 and 11, the number will be divisible by their product 99 also.

If a number is not divisible by 9 or 11, it is not divisible by 99

You must learn Divisibility Rules to say whether a given number is divisible by another number

without actually performing the division. Please go through divisibility rules before proceeding

further.

115929 is divisible by both 9 and 11 => 115929 is divisible by 99

115939 is not divisible by 9 and 11 => 115939 is not divisible by 99

115919 is not divisible by 9 and 11 => 115919 is not divisible by 99

115909 is not divisible by 9 and 11 => 115909 is not divisible by 99

Hence, 115929 is the answer

3) Answer : Option A

Explanation :

nth term of a geometric progression (G.P.)

tn=arn−1

where tn = nth term, a= the first term , r = common ratio, n = number of terms

Read more…
a=4r=84=2tn=1024tn=arn−1⇒1024=4×2n−1⇒2n−1=10244=25 6=28⇒2n−1=28⇒n−1=8⇒n=8+1=9
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January 19th, 2016

What percentage of numbers from 1 to 70 have 1 or 9 in the unit's digit?

A. 1
B. 14
C. 20
D. 21

Answer: Option C

Explanation:

Clearly, the numbers which have 1 or 9 in the unit's digit, have squares that end in the digit 1. Such numbers from 1 to 70 are 1, 9, 11, 19, 21, 29, 31, 39, 41, 49, 51, 59, 61, 69.

Number of such number =14

Required percentage = [14/70 * 100] % = 20%

In a certain school, 20%u0025 of students are below 8 years of age. The number of students above 8 years of age is of the number of students of 8 years of age which is 48. What is the total number of students in the school?

A. 72
B. 80
C. 120
D. 150
E. 100

Answer: Option E

Explanation:

Let the number of students be x. Then,

Number of students above 8 years of age = (100 - 20)% of x = 80% of x.

80% of x = 48 + 2/3 of 48

[80/100]x = 80

x = 100

Last edited by kartik; January 20th, 2016 at 05:04 PM..
   
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