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Q:

Two cubes have their volumes in the ratio 1 : 27. Find the ratio of their surface areas.

A) 2:9	B) 3:9
C) 1:9	D) 4:9

Answer & Explanation Answer: C) 1:9

Explanation:

Let their edges be a and b. Then,

a3/b3 = 1/27 (or) (a/b)3 = (1/3)3 (or) (a/b) = (1/3).

\Ratio of their surface area = 6a2/6b2 = a2/b2 = (a/b)2 = 1/9, i.e. 1:9.

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Filed Under: Quantitative Aptitude - Arithmetic Ability

Q:

The diagonal of a cube is $6 \sqrt{3}$ cm. Find its surface area

A) 216 sq.cm	B) 316 sq.cm
C) 416 sq.cm	D) 516 sq.cm

Answer & Explanation Answer: A) 216 sq.cm

Explanation:

Let the edge of the cube be a.

so, the diagonal a $\sqrt{3}$ = $6 \sqrt{3}$

=> a=6

Surface area = $6 a^{2}$ = 6 x 6 x 6 = 216 sq.cm

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Filed Under: Volume and Surface Area

Q:

A bag contains 7 green and 5 black balls. Three balls are drawn one after the other. The probability of all three balls being green, if the balls drawn are not replaced will be:

A) 123/897	B) 23/67
C) 7/44	D) 12/45

Answer & Explanation Answer: C) 7/44

Explanation:

Here, n(E) = $7 C_{1} \times 5 C_{1} \times 5 C_{1}$

And, n(S) = $12 C_{1} * 11 C_{1} * 10 C_{1}$

P(S) = $\frac{7 * 6 * 5}{12 * 11 * 10}$ = 7/44

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Filed Under: Probability

Q:

In a race, the odd favour of cars P,Q,R,S are 1:3, 1:4, 1:5 and 1:6 respectively. Find the probability that one of them wins the race.

A) 319/420	B) 27/111
C) 114/121	D) 231/420

Answer & Explanation Answer: A) 319/420

Explanation:

$P (P) = \frac{1}{4}, P (Q) = \frac{1}{5}, P (R) = \frac{1}{6}, P (S) = \frac{1}{7}$
All the events are mutually exclusive hence,

Required probability = P(P)+P(Q)+P(R)+P(S)

$\frac{1}{4} + \frac{1}{5} + \frac{1}{6} + \frac{1}{7}$ = $\frac{319}{420}$

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Filed Under: Probability

Q:

Three houses are available in a locality. Three persons apply for the houses. Each applies for one house without consulting others. The probability that all the three apply for the same house is :

A) 2/9	B) 1/9
C) 8/9	D) 7/9

Answer & Explanation Answer: B) 1/9

Explanation:

One person can select one house out of 3= $3 C_{1}$ ways =3.

Hence, three persons can select one house out of 3 in 3 x 3 x 3 =9.

Therefore, probability that all thre apply for the same house is 1/9

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Filed Under: Probability

Q:

Find the cost of 96 shares of Rs. 10 each at $\frac{3}{4}$ discount, brokerage being 1/4 per share.

A) 912	B) 921
C) 920	D) 900

Answer & Explanation Answer: A) 912

Explanation:

Cost of 1 share = $R s . [(10 - \frac{3}{4}) + \frac{1}{4}] = R s \frac{19}{2}$

Cost of 96 shares = $R s . (\frac{19}{2} * 96)$ = Rs. 912.

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Filed Under: Stocks and Shares

Q:

The market value of a 10.5% stock, in which an income of Rs. 756 is derived by investing Rs. 9000, brokerage being 1/4%, is:

A) 108.25	B) 112.20
C) 124.75	D) 125.25

Answer & Explanation Answer: C) 124.75

Explanation:

For an income of Rs. 756, investment = Rs. 9000.

For an income of $R s . \frac{21}{2}$ , investment = $R s . \frac{9000}{756} \times \frac{21}{2}$ = Rs. 125.

For a Rs. 100 stock, investment = Rs. 125.

Market value of Rs. 100 stock = $R s . (125 - \frac{1}{4})$ = Rs. 124.75

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Filed Under: Stocks and Shares

Q:

A 12% stock yielding 10% is quoted at:

A) 67	B) 110
C) 112	D) 120

Answer & Explanation Answer: D) 120

Explanation:

To earn Rs. 10, money invested = Rs. 100.

To earn Rs. 12, money invested = $R s . (\frac{100}{10} * 12)$ = Rs. 120.

Market value of Rs. 100 stock = Rs. 120.

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Filed Under: Stocks and Shares

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