## Previous Year CAT Questions on Number System

1.553 + 173 - 723 is divisible by
a) both 3 and 13
b) both 7 and 17
c) both 3 and 17
d) both 7 and 13

Explanation: 2. Out of 128 boxes of oranges, each box contains at least 120 and at most 144 oranges. The number of boxes containing the same number of oranges is at least
a) 5
b) 103
c) 6
d) Cannot be determined

Explanation: 3. In a 4 - digit number, the sum of the first two digits is equal to that of the last two digits. The sum of the first and last digits is equal to the third digit. Finally, the sum of the second and fourth digits is twice the sum of the other two digits. What is the third digit of the number?
a) 5
b) 8
c) 1
d) 4

Explanation: 4. Anita had to do a multiplication. Instead of taking 35 as one of the multipliers, she took 53. As a result, the product went up by 540. What is the new product?
a) 1050
b) 540
c) 1440
d) 1590

Explanation: 5. In a number system the product of 44 and 11 is 3414. The number 3111 of this system, when converted to the decimal number system, becomes
a) 406
b) 1086
c) 213
d) 691

Explanation: 6. Every ten years the Indian government counts all the people living in the country. Suppose that the director of the census has reported the following data on two neighbouring villages Chota Hazri and Mota Hazri
Chota Hazri has 4,522 fewer males than Mota hazri.
Mota Hazri has 4,020 more females than males.
Chota Hazri has twice as many females as males.
Chota Hazri has 2,910 fewer females than Mota Hazri.
What is the total number of males in Chota Hazri?
a) 11264
b) 14174
c) 5632
d) 10154

Explanation: 7. Let x, y and z be distinct integers. x and y are odd positive, and z is even positive. Which one of the following statements can not be true?
a) $\left(x-z\right)^{2}$ y is even
b) (x-z) y2 is odd
c) (x – z)y is odd
d) $\left(x-y\right)^{2}$ z is even

Explanation: 8. Number S is obtained by squaring the sum of digits of a two digit number D. If difference between S and D is 27, then the two digit number D is
a) 24
b) 54
c) 34
d) 45

Explanation: 9. When $2^{256}$ is divided by 17 the remainder would be
a) 1
b) 16
c) 14
d) None of these 10. At a book store, “MODERN BOOK STORE” is flashed using neon lights. The words are individually flashed at intervals of $2\frac{1}{2},4\frac{1}{4},5\frac{1}{8}$  seconds respectively, and each word is put off after a second. The least time after which the full name of the bookstore can be read again is 