# CAT Number System Questions for Practice

Question 1:
x and y are real numbers satisfying the conditions 2 < x < 3 and – 8 < y < –7. Which of the following expressions will have the least value?
Topic: Basics

[1] x2y
[2] xy2
[3] 5xy
[4] None of these

Question 2:
Three friends, returning from a movie, stopped to eat at a restaurant. After dinner, they paid their bill and noticed a bowl of mints at the front counter. Sita took one-third of the mints, but returned four because she had a momentary pang of guilt. Fatima then took one-fourth of what was left but returned three for similar reason. Eswari then took half of the remainder but threw two back into the bowl. The bowl had only 17 mints left when the raid was over. How many mints were originally in the bowl?
Topic: Basics

[1] 38
[2] 31
[3] 41
[4] None of these

Question 3:
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
Topic: Base System

[1] 406
[2] 1086
[3] 213
[4] 691

Question 4:
Every 10 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 ChotaHazri and MotaHazri.

ChotaHazri has 4,522 fewer males than MotaHazri.

MotaHazri has 4,020 more females than males.

ChotaHazri has twice as many females as males.

ChotaHazri has 2,910 fewer females than MotaHazri.

What is the total number of males in ChotaHazri?

Topic: Basics

[1] 11264
[2] 14174
[3] 5632
[4] 10154