Arithmetic(Exams > Cat > Quantitaitve Aptitude ) Questions and answers for exam Preparation

Exams > Cat > Quantitaitve Aptitude

ARITHMETIC MCQs

Total Questions : 147 | Page 14 of 15 pages

In a class there are 200 students, at least 140 of students like Maths, at least 150 like Science and at least 160 like English. What is the minimum number of students who like all three subjects?

Discuss Question

Answer: Option A. -> 50
:
A

X = I + II + III = 200

S = I + 2II + 3III = 140 + 150 + 160 = 450

S – X = II + 2III = 450 – 200 = 250

For III to be the minimum, II has to be the maximum. Now, II can take the maximum value of 200.

So, minimum value of III = 250 – 200= 50.

Question 132.

In a survey among 70 people, 50 like Vanila and 40 like Chocolate. What is the minimum and maximum number of people who like exactly 2 flavours respectively?

50, 50
20, 40
20, 20
30, 20

Discuss Question

Answer: Option C. -> 20, 20
:
C

X = I + II = 70

S = I + 2II = 50 + 40 = 90

S – X = II = 90 – 70 = 20 = x

So, minimum and maximum value of x = 20.

Question 133.

Ram and Shyam invest Rs.15,000 and Rs.25,000, respectively, in a business and at the end of the year , make a profit of Rs.10,000. They agree to re-invest $12 %$ of profit. Out of the remaining profit, each of them takes Rs.1000 and rest is divided in the ratio of their original investment. Find Ram’s total share in the profit.

Rs. 4250
Rs.3000
Rs.2550
Rs.3550

Discuss Question

Answer: Option D. -> Rs.3550
:
D

$12 %$ of profit = 1200

Remaining = 8800

After taking 1000 each, amount remaining = 6800

Ratio of shares of Ram and Shyam = 15,000 : 25,000 = 3 : 5

Ram’s share $= \frac{3}{8} \times 6800 = 2550$

Ram’s profit = 2550 + 1000 = 3550.

Question 134.

A bottle contains $100 %$ phenyl. $\frac{1}{3}$ of it is replaced with water. The operation is repeated 4 times. What is the ratio of phenyl: water after the last operation?

16:81
1:5
14:82
None of these

Discuss Question

Answer: Option D. -> None of these
:
D

Option (d)

$\frac{L i q u i d A l e f t t a k e n n^{t h} o p e r a t i o n}{I n i t i a l q u a n t i t y o f A i n t h e v e s s e l} = \frac{(a - b)^{n}}{a^{n}}$

Amount of phenyl remaining $= {(1 - \frac{1}{3})}^{4} = \frac{16}{81}$

Therefore, ratio or phenyl:water = 16:65. (81-16=65)

Question 135.

A man purchased 40 kg of cotton at a rate of Rs 65 per kg. then he extracted $20 %$ waste(by weight) from it so that the quality of the cotton improved and he was able to sell them at Rs.80 per kg. Also the waste had $60 %$ cotton seed by weight which he was able to sell Rs.20 per kg. what $%$ profit did he make?

$8.65 %$
$1.24 %$
$1.47 %$
$2.15 %$

Discuss Question

Answer: Option D. ->

2.15 %

:
D

wt = 40 kg
cost = Rs.65/kg
Total cost $= 40 \times 65$
= Rs 2600
SP $\to$
wt after $20 %$ is extracted
$\Rightarrow$ 32 kg
Selling cost = 32 $\times$ 80
= Rs 2560
$60 %$ of waste $= \frac{60}{100} \times 8 = 4.8 k g$
selling price $= 4.8 \times 20$
= 96
Total price = 2656
Profit $= \frac{56}{2600} \times 100 = 2.15 %$

Question 136.

In an online poll for the title of “Miss photogenic”, the winner gets 40 votes more than the one who comes second and 75 votes more than the person who comes $3^{r d}$ . there are only 3 candidates. The winner and her nearest competitor polled an average of 90 votes together. How many votes were totally cast online, assuming that there are no invalid votes?

Discuss Question

Answer: Option B. -> 215
:
B

Winner gets 40 votes more the person who came second and the average is 90 $\Rightarrow$ winner = 110 votes
second person = 70 votes
Total votes = 110 + 70 + 35
= 215

Question 137.

At the end of year 1998, Ramesh bought 108 shares. Henceforth, every year he added $p %$ of the shares at the beginning of the year and sold $q %$ of the shares at the end of the year where p $>$ 0 and q $>$ 0. If Ramesh had 108 shares at the end of year 2002, after making the sales for that year, which of the following is true?

p = q
$p < q$
$p > q$
$p = \frac{q}{2}$

Discuss Question

Answer: Option C. ->

p > q

:
C

If the numbers of shares remain constant, then p has to be greater than q. Because, we are taking $p %$ on base price after getting increased we take $q %$ of that, which is greater than the base price. Answer is option (c).

Question 138.

1200
1600
2000
None of these

Discuss Question

Answer: Option D. -> None of these
:
D

OPTION D

Given that $\frac{P N R}{100} = 900$

$3600 \times 5 \times \frac{r}{100} = 900$

$R = 5 %$

He will split the amount exactly in half. Therefore $\frac{3600}{2} = 1800$ will be the amount invested

Question 139.

How many kilograms of rice costing 3.6 per kg should be mixed with 8 kgs of rice costing 4.20 per kg, such that the mixture yields a profit of $10 %$ when it is sold at 4.40 per kg?

5 kgs
6 kgs
3 kgs
4 kgs

Discuss Question

Answer: Option D. -> 4 kgs
:
D

For all alligation questions, remember that we need to consider only the cost price

Given that the Selling Price = .

$C o s t p r i c e \times 1.1 = S e l l i n g p r i c e$

$C o s t p r i c e = \frac{S e l l i n g p r i c e}{1.1} = \frac{4.4}{1.1} = 4 r s$

Ratio of quantity of rice = 2:4 or 1:2. Given that the quantity of the second variety is 8 kg, the first variety should be $\frac{8}{2}$ =4 kgs

Question 140.

There is a bottle of coke. $25 %$ is replaced by pepsi. Again $25 %$ is replaced by Pepsi and finally another $25 %$ is replaced by Pepsi. What is the approximate final $%$ of coke in the bottle?

Discuss Question

Answer: Option C. -> 42
:
C

Option (c)

Let the bottle contain 100 units of liquid.

Liquid taken out in each case is $25 %$

The final quantity of component from the original mixture that is not being replaced, if this operation is repeated 3 times, is $100 (1 - \frac{25}{100})^{3}$