CAT Questions

Q:

What was the day on 15th august 1947 ?

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

Explanation:

15 Aug, 1947 = (1946 years + Period from 1.1.1947 to 15.8.1947)

Odd days in 1600 years = 0

Odd days in 300 years = 1

46 years = (35 ordinary years + 11 leap years) = (35 x 1 + 11 x 2)= 57 (8 weeks + 1 day) = 1 odd day

Jan.   Feb.   Mar.   Apr.   May.   Jun.   Jul.   Aug

( 31 + 28 + 31 + 30 + 31 + 30 + 31 + 15 ) = 227 days = (32 weeks + 3 days) = 3 odd days.

Total number of odd days = (0 + 1 + 1 + 3) = 5 odd days.

Hence, as the number of odd days = 5 , given day is Friday.

509 81069
Q:

Tea worth of Rs. 135/kg & Rs. 126/kg are mixed with a third variety in the ratio 1: 1 : 2. If the mixture is worth Rs. 153 per kg, the price of the third variety per kg will be____?

 A) Rs. 169.50 B) Rs.1700 C) Rs. 175.50 D) Rs. 180

Explanation:

Since first second varieties are mixed in equal proportions, so their average price = Rs.$\inline \fn_jvn \small \left ( \frac{126+135}{2} \right )$ = Rs.130.50

So, Now the mixture is formed by mixing two varieties, one at Rs. 130.50 per kg and the other at say Rs. 'x' per kg in the ratio 2 : 2, i.e., 1 : 1. We have to find 'x'.

Cost of 1 kg tea of 1st kind         Cost of 1 kg tea of 2nd kind

x-153/22.50 = 1  => x - 153 = 22.50  => x=175.50.

Hence, price of the third variety = Rs.175.50 per kg.

33 33770
Q:

The diluted wine contains only 8 liters of wine and the rest is water. A new mixture whose concentration is 30%, is to be  formed by replacing wine. How many liters of mixture shall be replaced with pure wine if there was initially 32 liters of water in the mixture ?

 A) 4 B) 5 C) 8 D) None of these

Explanation:

Wine                         Water

8L                              32L

1                :               4

20 %                           80% (original ratio)

30 %                           70% (required ratio)

In  ths case, the percentage of water being reduced when the mixture is being replaced with wine.

so the ratio of left quantity to the initial quantity is 7:8

Therefore , $\inline \fn_jvn \frac{7}{8}=\left [ 1-\frac{K}{40} \right ]$

=> $\inline \fn_jvn \frac{7}{8}=\left [ \frac{40-K}{40} \right ]$ = K = 5 Lit

16 3672
Q:

A man is facing north-west. He turns $\inline 90^{o}$ in the clockwise direction, then $\inline 180^{o}$ in the anticlockwise direction and then another $\inline 90^{o}$ in the same direction. Which direction is he facing now?

 A) South B) South-west C) South-east D) East

Explanation:

As shown in fig. the man initially faces in the direction OP. On moving $\inline 90^{o}$ clockwise, he faces in the direction OX. On further moving $\inline 180^{o}$ anticlockwise, he faces in the direction OY. Finally, on moving $\inline 90^{o}$ anticlockwise, he faces in the direction OZ, which is South-east.

19 3098
Q:

There are three rooms in a Hotel: one single, one double and one for four persons. How many ways are there to house seven persons in these rooms ?

 A) 105 B) 7! x 6! C) 7!/5! D) 420

= 7 x $\inline \fn_jvn \small \frac{6x5}{2}$ x 1