6500+ Quantitative Aptitude Questions and Answers With Explanation

Q:

If the mean of a, b, c is M and ab + bc + ca = 0, then the mean of $\frac{a^{2} + b^{2} + c^{2}}{3}$ is :

A) M	B) 3 M^2
C) 2 (M/3)	D) M^2

Answer & Explanation Answer: B) 3 M^2

Explanation:

We have : ( a + b + c) / 3 = M or (a + b + c) = 3M.

Now. ${(a + b + c)}^{2} = {(3 M)}^{2} = 9 M^{2}$ .

$< = > a^{2} + b^{2} + c^{2} + 2 (a b + b c + c a) = 9 M^{2}$

$a^{2} + b^{2} + c^{2} = 9 M^{2}, (a b + b c + c a = 0)$

Required mean = $(\frac{a^{2} + b^{2} + c^{2}}{3}) = \frac{9 M^{2}}{3} = 3 M^{2}$ .

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Filed Under: Average
Exam Prep: AIEEE , Bank Exams , CAT
Job Role: Bank Clerk , Bank PO

35 28491

Q:

Three numbers are in the ratio 4 : 5 : 6 and their average is 25. The largest number is :

A) 30	B) 40
C) 50	D) 60

Answer & Explanation Answer: A) 30

Explanation:

Let the numbers be 4x, 5x and 6x, Then, (4x + 5x + 6x ) / 3 = 25

=> 5x = 25

=> x = 5.

Largest number 6x = 30.

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Filed Under: Problems on Numbers

39 28461

Q:

In the following question, select the odd letter/letters from the given alternatives.

A) CHM	B) GLQ
C) KPV	D) NSX

Answer & Explanation Answer: C) KPV

Explanation:

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Filed Under: Odd Man Out
Exam Prep: Bank Exams

0 28412

Q:

A sum of Rs. 725 is lent in the beginning of a year at a certain rate of interest. After 8 months, a sum of Rs. 362.50 more is lent but at the rate twice the former. At the end of the year, Rs. 33.50 is earned as interest from both the loans. What was the original rate of interest?

A) 3.46%	B) 4.5%
C) 5%	D) 6%

Answer & Explanation Answer: A) 3.46%

Explanation:

Let the original rate be R%. Then, new rate = (2R)%.

Note: Here, original rate is for 1 year(s); the new rate is for only 4 months i.e.1/3 year(s).

$(\frac{725 * R * 1}{100}) + (\frac{362.50 * 2 R * 1}{100 * 3}) = 33.50$

=> (2175 + 725) R = 33.50 x 100 x 3

=> (2175 + 725) R = 10050

=> (2900)R = 10050

=> $R = \frac{10050}{2900} = 3.46$

Original rate = 3.46%

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Filed Under: Simple Interest
Exam Prep: GRE

37 28405

Q:

In the figure $∠ AMB = 130 °$ , then what is the value (in deg) of $∠ ABQ$ ?

A) 40	B) 50
C) 60	D) 90

Answer & Explanation Answer: B) 50

Explanation:

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Filed Under: Volume and Surface Area
Exam Prep: Bank Exams

3 28308

Q:

A bag contains 4 red and 3 black balls. A second bag contains 2 red and 4 black balls. One bag is selected at random. From the selected bag, one ball is drawn. Find the probability that the ball drawn is red.

A) 23/42	B) 19/42
C) 7/32	D) 16/39

Answer & Explanation Answer: B) 19/42

Explanation:

A red ball can be drawn in two mutually exclusive ways

(i) Selecting bag I and then drawing a red ball from it.

(ii) Selecting bag II and then drawing a red ball from it.

Let E1, E2 and A denote the events defined as follows:

E1 = selecting bag I,

E2 = selecting bag II

A = drawing a red ball

Since one of the two bags is selected randomly, therefore

P(E1) = 1/2 and P(E2) = 1/2

Now, $P (\frac{A}{E_{1}})$ = Probability of drawing a red ball when the first bag has been selected = 4/7

$P (\frac{A}{E_{2}})$ = Probability of drawing a red ball when the second bag has been selected = 2/6

Using the law of total probability, we have

P(red ball) = P(A) = $P (E_{1}) \times P (\frac{A}{E_{1}}) + P (E_{2}) \times P (\frac{A}{E_{2}})$

= $\frac{1}{2} \times \frac{4}{7} + \frac{1}{2} \times \frac{2}{6} = \frac{19}{42}$

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Filed Under: Probability
Exam Prep: AIEEE , Bank Exams , CAT , GATE
Job Role: Analyst , Bank Clerk , Bank PO

64 28305

Q:

There are four hotels in a town. If 3 men check into the hotels in a day then what is the probability that each checks into a different hotel?

A) 1/2	B) 3/4
C) 4/7	D) 3/8

Answer & Explanation Answer: D) 3/8

Explanation:

Total cases of checking in the hotels = 4 x 4 x 4 = 64 ways.

Cases when 3 men are checking in different hotels = 4×3×2 = 24 ways.

Required probability =24/64 = 3/8

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Filed Under: Probability

46 28297

Q:

Select the odd figure out of the given series.

A) 2	B) 3
C) 4	D) 1

Quantitative Aptitude - Arithmetic Ability Questions

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