GATE Questions and Answers with Explanation

Q:

A letter is takenout at random from 'ASSISTANT' and another is taken out from 'STATISTICS'. The probability that they are the same letter is :

A) 35/96	B) 19/90
C) 19/96	D) None of these

Answer & Explanation Answer: B) 19/90

Explanation:

$A S S I S T A N T \to A A I N S S S T T$

$S T A T I S T I C S \to A C I I S S S T T T$

Here N and C are not common and same letters can be A, I, S, T. Therefore

Probability of choosing A = $\frac{2_{C_{1}}}{9_{C_{1}}} \times \frac{1_{C_{1}}}{10_{C_{1}}}$ = 1/45

Probability of choosing I = $\frac{1}{9_{C_{1}}} \times \frac{2_{C_{1}}}{10_{C_{1}}}$ = 1/45

Probability of choosing S = $\frac{3_{C_{1}}}{9_{C_{1}}} \times \frac{3_{C_{1}}}{10_{C_{1}}}$ = 1/10

Probability of choosing T = $\frac{2_{C_{1}}}{9_{C_{1}}} \times \frac{3_{C_{1}}}{10_{C_{1}}}$ = 1/15

Hence, Required probability = $\frac{1}{45} + \frac{1}{45} + \frac{1}{10} + \frac{1}{15} = \frac{19}{90}$

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Filed Under: Probability
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97 22689

Q:

The largest measuring cylinder that can accurately fill 3 tanks of capacity 98, 182 and 266 litres each, is of capacity ?

A) 7 lts	B) 14 lts
C) 98 lts	D) 42 lts

Answer & Explanation Answer: B) 14 lts

Explanation:

To know the the measuring cylinder that can fill all the given capacities , they must be divisible by the required number.

98,182,266 all are divisible by 14
So 14 litres is the largest cylinder that can fill all the given cylinders.

(or)

The other method is take HCF of all given capacities i.e 98, 182 and 266.

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Filed Under: HCF and LCM
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21 22591

Q:

Equal quantities of three mixtures of milk and water are mixed in the ratio 1:2, 2:3 and 3:4. The ratio of water and milk in the mixture is ?

A) 193 : 122	B) 97 : 102
C) 115 : 201	D) 147 : 185

Answer & Explanation Answer: A) 193 : 122

Explanation:

Given the three mixtures ratio as (1:2),(2:3),(3:4)

(1+2),(2+3),(3+4)

Total content = 3,5,7

Given equal quantities of the three mixtures are mixed, then LCM of 3, 5, 7 = 105

105/3 = 35 , 105/5 = 21 , 105/7 = 15

Now, the individual equal quantity ratios are (35x1, 35x2), (21x2, 21x3), (15x3, 15x4)

i.e (35,70), (42,63), (45,60)

So overall mixture ratio of milk and water is

35+42+45 : 70+63+60

122:193

But in the question asked the ratio of water to milk = 193 : 122

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Filed Under: Alligation or Mixture
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27 22442

Q:

If yesterday were tomorrow, then today would be Friday. What day is today?

A) Saturday	B) Monday
C) Sunday	D) Tuesday

Answer & Explanation Answer: C) Sunday

Explanation:

If yesterday were tomorrow, today is Friday => tomorrow of friday is Saturday.

Hence, it implies that today is Sunday if tomorrow is Saturday.

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Filed Under: Calendar
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86 22440

Q:

Ajay and Vijay have some marbles with them. Ajay told Vijay "if you give me 'x' marbles, both of us will have equal number of marbles". Vijay then told Ajay "if you give me twice as many marbles, I will have 30 more marbles than you would". Find 'x' ?

A) 4	B) 10
C) 8	D) 5

Answer & Explanation Answer: D) 5

Explanation:

If Vijay gives 'x' marbles to Ajay then Vijay and Ajay would have V - x and A + x marbles.
V - x = A + x --- (1)
If Ajay gives 2x marbles to Vijay then Ajay and Vijay would have A - 2x and V + 2x marbles.
V + 2x - (A - 2x) = 30 => V - A + 4x = 30 --- (2)
From (1) we have V - A = 2x
Substituting V - A = 2x in (2)
6x = 30 => x = 5.

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Filed Under: Arithmetical Reasoning
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29 22313

Q:

What value should come in place of the question mark (?) in the following question?

$325 - 12^{2} + 75 = ?^{2} - 68$

A) 18	B) 324
C) 18	D) 3242

Answer & Explanation Answer: C) 18

Explanation:

$?^{2}$ = 325 – 144 + 75 + 68
= 468 – 144 = 324
(?) = 18,-18

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Filed Under: Quantitative Aptitude - Arithmetic Ability
Exam Prep: Bank Exams , GATE

0 22291

Q:

A number is increased by 20% and then decreased by 20%, the final value of the number is ?

A) increase by 2%	B) decrease by 3%
C) decrease by 4%	D) increase by 5%

Answer & Explanation Answer: C) decrease by 4%

Explanation:

Here, x = 20 and y = - 20
Therefore, the net % change in value
= $x + y + \frac{x y}{100}$ %
= $20 + (- 20) + \frac{20 \times - 20}{100}$ % or - 4%

Since the sign is negative, there is a decrease in value by 4%.

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Filed Under: Percentage
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34 22185

Q:

Yard is to Inch as Quart is to

A) Milk	B) Gallon
C) Liquid	D) Ounce

Answer & Explanation Answer: D) Ounce

Explanation:

Yard is to Inch as Quart is to Ounce.

Because Yard and Inch are units of measurement Where Yard is larger than Inch i.e, 1 Yard = 36 Inches.

So, here Quart and Ounce are also units of measurement where Quart is larger than Ounce i.e, 1 Quart = 32 Ounces.

Gallon is not correct because Gallon is larger than Quart and Milk and Liquid are not units of measurement.

So, Ounce is correct.

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Filed Under: Analogy
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21 22163

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