Quantitative Aptitude Test

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Quantitative Aptitude Test - 4

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Weekly Quiz Competition

Question 1
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Which of the following is a perfect square?

A
97,474

B
1,23,301

C
1,37,641

D
1,70,567

Solution

We need to find the square root of all the given numbers.
Only option (C) has an integral square root as 371 i.e. √1,37,641 = 371.
For other option we won't get an integer as square root.
Hence, the correct option is (c).
Question 2
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The 5th and 9th terms of a harmonic progression are $\frac{2}{3}$ and $\frac{2}{9}$ respectively. What is the first term of the progression?

A
-3.5

B
-1.5

C
-0.67

D
0

Solution

As, the terms are in H.P. so, their inverse must be in A.P. (Arithmetic progression)

So, 3/2 and 9/2 are the 5th and 9th terms of the A.P. ,and we know if a and d are 1st term and common difference of A.P., then 9th term-5th term = 4d = 9/2 – 3/2.

So, d = 3/4

Now, the 1st term of A.P. = 5th term – 4d =

Hence, the 1st term of H.P. must be the inverse of 1st term of A.P. and so, the 1st term of H.P. is

Hence, the correct option is (c).
Question 3
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The positive integral divisors k1, k2, k3, … of a positive integer n are given in ascending order. If 11 divides n and n = k5 + k6 + k7, what is the value of n?

A
6

B
36

C
42

D
66

Solution

Also, the number n will have total of 8 divisors including 1 and itself (since k7 = n/2, k8 = n ).
Since n is divisible by three primes 2, 3 and 11, the only possibility for it to have 8 divisors is for it to be the product of the three primes, that is 66.

Hence, the correct option is (d).
Question 4
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Four clocks were set right at the same time. One clock gains 'a' minutes in a day, second clock loses 'b' minutes in a day, third clock gains 'c' minutes in a day and the fourth clock gains 'd' minutes. After how much time will all the clocks again show the correct time simultaneously if a + b + c + d = 1 hour, a : b = c : d = 2 : 1 and b : d = 3 : 1?

A
3 hours

B
12 hours

C
24 hours

D
144 days

Solution
Question 5
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On January 1, Ajit put Re 1 in his piggy bank. Every day, he put in Rs 2 more than the total amount of money already in the piggy bank. Which of the following expressions gives the total amount of money in Ajit's piggy bank at the end of January?

A
2³⁰

B
3(2³⁰) – 2

C
2³¹

D
3(2³⁰)

Solution

Ajit puts Re 1 on January 1, Rs 3 on January 2, Rs. 6 on January 3, Rs. 12 on January 4 and so on.

So, the series is 1+3+6+12+24+… The 2nd to 31st term are in G.P. with 1st term 3 and common ratio = 2

So, total money in Ajit's piggy bank at the end of January is sum of series 1+3+6+12+24… = 1+ sum of 30 terms of G.P. with 1st term and common ratio 3 and 2 respectively.

So, amount at the end of January = s 1+ 3(230-1)/(2-1) = 1+3(230-1) = 1+3(2³⁰)-3 = 3(2³⁰)-2.

Hence, the correct option is (b).
Question 6
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In a shop, there are 500 sweet products 210 are biscuit-based, 160 are milk-based and 160 are coconut-based. 80 have both milk and coconut but no biscuit, 70 have milk and biscuit but no coconut, 60 have biscuit and coconut but no milk. How many items have all three ingredients if 200 have none of these ingredients?

A
10

B
30

C
50

D
130

Solution

Total = 500
Biscuit based = 210
Milk based = 160
Coconut based = 160
Milk and coconut = 80
Milk and biscuit = 70
Biscuit and coconut = 60
All three = x
None = 200
Now, the formula is Total – None = A + B + C – ( AB + BC + CA) – 2(ABC)
Or, 500 – 200 = 210 + 160 + 160 – (80 + 70 + 60) – 2x
Or, 300 = 530 – 210 – 2x
Or, 2x = 320 – 300
Or, x = $\frac{20}{2}$ = 10
Hence, the correct option is (a).
Question 7
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A candidate who gets $20 \%$ marks fails by 10 marks but another candidate who gets $42 \%$ marks gets $12 \%$ more than the passing marks. Find the maximum marks.

A
50

B
100

C
150

D
200

Solution

From the given statement pass percentage is $42 \%-12 \%=30 \%$
Let the maximum marks be x
By hypothesis, $30 \%$ of $x-20 \%$ of $x=10$ marks
i.e., $10 \%$ of $x=10$
Therefore, $x=100$ marks.
Question 8
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There are 5 identical circles within a circle as shown below. P, Q, R and S are the respective centres of four of these circles. If the radius of the bigger circle is 15 cm, what is the area of the shaded portion?

A
(200 – 20π) cm²

B
(200 – 25π) cm²

C
(200 – 40π) cm²

D
(200 – 50π) cm²

Solution
Question 9
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The production of rice increased by 75% from 1990 to 1995. From 1995 to 2000, there was a 100% increase. What is the percentage increase in the production of rice from 1990 to 2000?

A
250%

B
280%

C
285%

D
290%

Solution

Let the production of rice in 1990 be 100 tonnes.
Then, the production of rice in 1995 = 100 x 1.75 = 175 tonnes And the production of rice in 2000 = 175 x 2 = 350 tonnes
Thus the percentage increase in production from 1990 to 2000 = $\frac{(350 - 100)}{100}$ x 100 = 250% .
Hence, the correct option is (a).
Question 10
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Fahim and Farhan together earned Rs 37,570 from a business venture. They divided it and each deposited his share in a bank. At the end of 9 years, the amount Farhan had in the bank was the same as the amount Fahim had at the end of 7 years. If the interest was compounded annually at 10% per annum, what was Farhan's share of the money earned from the business venture?

A
Rs 14,174

B
Rs 16,437

C
Rs 17,000

D
Rs 18,785

Solution

Let the share of Farhan be x, then share of Fahim must be (37,570 – x)
Now, both invested money at the same compound rate at an interest of 10%
According to given condition,
x(1+10%)9 = (37,570-x)(1+10%)7
So, x(1+10%)2 = 37,570 –x
So, x(1+10%)2 = 37,570 – x
21x= 37,570- x
Solving it we get x = Rs.17,000.
Hence, the correct option is (c).