# GATE Questions

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

8 4494
Q:

The sum of three consecutive multiples of 3 is 72. What is the second largest number ?

 A) 27 B) 24 C) 21 D) 42

Explanation:

Let the numbers be 3x, 3x + 3 and 3x + 6.
Then,
3x + (3x + 3) + (3x + 6) = 72
9x = 63
x = 7
Largest number = 3x + 6 = 27.

=> Second largest number = 27 - 3 = 24

13 4446
Q:

In a scheme, a pack of three soaps with MRP Rs.45 is available for Rs.42. If it still gives a profit of 5% to the shopkeeper, then the cost price of the pack is ?

 A) 38 B) 39 C) 40 D) 41

Explanation:

Given M.P=45,S.P=42, Profit = 0.05

Let C.P=x , Then

Profit = (42-x)/x = 0.05
=> x = 40.

5 4440
Q:

A letter lock consists of three rings each marked with six different letters. The number of distinct unsuccessful attempts to open the lock is at the most  ?

 A) 215 B) 268 C) 254 D) 216

Explanation:

Since each ring consists of six different letters, the total number of attempts possible with the three rings is = 6 x 6 x 6 = 216. Of these attempts, one of them is a successful attempt.

Maximum number of unsuccessful attempts = 216 - 1 = 215.

4 4391
Q:

4 men can repair a road in 7 hours. How many men are required to repair the road in 2 hours ?

 A) 17 men B) 14 men C) 13 men D) 16 men

Answer & Explanation Answer: B) 14 men

Explanation:

M x T / W = Constant
where, M= Men (no. of men)
T= Time taken
So, here we apply
M1 x T1/ W1 = M2 x T2 / W2
Given that, M1 = 4 men, T1 = 7 hours ; T2 = 2 hours, we have to find M2 =?
Note that here, W1 = W2 = 1 road, ie. equal work load.
Clearly, substituting in the above equation we get, M2 = 14 men.

3 4324
Q:

How many different words can be made using the letters of the word ' HALLUCINATION ' if all constants are together?

 A) 129780 B) 1587600 C) 35600 D) None of these

Explanation:

H   L   C   N    T    A   U   I   O

L        N          A        I

There are total 131 letters out of which 7 are consonants and 6 are vowels. Also ther are 2L's , 2N's, 2A's and 2I's.

If all the consonants  are together then the numberof arrangements = $\frac{\mathbf{7}\mathbf{!}}{\mathbf{2}\mathbf{!}}$x 1/2! .

But the 7 consonants  can be arranged themselves in  $\frac{\mathbf{7}\mathbf{!}}{\mathbf{2}\mathbf{!}}$ x 1/2! ways.

Hence the required number of ways = ${\left(\frac{7!}{2!2!}\right)}^{2}$ = 1587600

2 4263
Q:

How many parallelograms will be formed if 7 parallel horizontal lines intersect 6 parallel vertical lines?

 A) 215 B) 315 C) 415 D) 115

Explanation:
Parallelograms are formed when any two pairs of parallel lines (where each pair is not parallel to the other pair) intersect.

Hence, the given problem can be considered as selecting pairs of lines from the given 2 sets of parallel lines.

Therefore, the total number of parallelograms formed = 7C2 x 6C2 = 315

12 4233
Q:

Given that on 9th August 2016 is Saturday. What was the day on 9th August 1616 ?

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