# CAT Number system Practice Problems Set 08

Question 1:
Amol was asked to calculate the arithmetic mean of 10 positive integers, each of which had 2 digits. By mistake, he interchanged the 2 digits, say a and b, in one of these 10 integers. As a result, his answer for the arithmetic mean was 1.8 more than what it should have been. Then b – a equals
Topic: Digits

[1] 1
[2] 2
[3] 3
[4] None of these

Question 2:
A child was asked to add first few natural numbers (i.e. 1 + 2 + 3 + …) so long his patience permitted. As he stopped, he gave the sum as 575. When the teacher declared the result wrong, the child discovered he had missed one number in the sequence during addition. The number he missed was
Topic: Basics

[1] less than 10
[2] 10
[3] 15
[4] more than 15

Question 3:
When 2256 is divided by 17, the remainder would be
Topic: Remainders

[1] 1
[2] 16
[3] 14
[4] None of these

Question 4:
At a bookstore, ‘MODERN BOOK STORE’ is flashed using neon lights. The words are individuallyflashed at the intervals of $2\frac{1}{2}s,4\frac{1}{4}s{\rm{\; and\; }}5\frac{1}{8}s$ 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
Topic: HCF LCM

[1] 49.5 s
[2] 73.5 s
[3] 1744.5 s
[4] 855 s

Question 5:
Three pieces of cakes of weights $4\frac{1}{2}lb{\rm{, }}6\frac{3}{4}lb{\rm{\;and\;}}7\frac{1}{5}{\rm{lb}}$ respectively are to be divided into parts of equal weight. Further, each part must be as heavy as possible. If one such part is served to each guest, then what is the maximum number of guests that could be entertained?
Topic: HCF LCM

[1] 54
[2] 72
[3] 20
[4] None of these

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