Number Theory Previous Year Questions (CAT)  Set 0025

Previous years`s CAT questions: Number Theory
Post your solutions as reply to respective questions below.

Question 1
Let x, y and z be distinct integers, x and y are odd and positive, and z is even and
positive. Which one of the following statements cannot be true?
1. (x – z)^{2}y is even
2. (x – z)y^{2} is odd
3. (x – z)y is odd
4. (x – y)^{ 2}z is even (CAT 2001)

Question 2
If x > 5 and y < –1, then which of the following statements is always true?
1. (x + 4y) > 1
2. x > –4y
3. –4x < 5y
4. None of these (CAT 2001)

Question 3
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?
1. 1050
2. 540
3. 1440
4. 1590 Â Â (CAT 2001)

Question 4
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?
1. x^{2}y
2. xy^{2}
3. 5xy
4. None of these (CAT 2001)

Question 5
m is the smallest positive integer such that for any integer n ≥m, the quantity n^{3} – 7n^{2} +11n – 5 is positive. What is the value of m?
1. 4
2. 5
3. 8
4. None of these (CAT 2001)

Question 6
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 1/3 of the mints, but returned four because she had a momentary pang of guilt. Fatima then took 1/4 of what was left but returned three for similar reasons. 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?
1. 38
2. 31
3. 41
4. None of these (CAT 2001)

Question 7
Â (CAT 2001)

Answer: Option 4

Question 8
There were a hundred schools in a town. Of these, the number of schools having a play â ground was 30, and these schools had neither a library nor a laboratory. The number of schools having a laboratory alone was twice the number of those having a library only. The number of schools having a laboratory as well as a library was one fourth the number of those having a laboratory alone. The number of schools having either a laboratory or a library or both was 35.
What was the ratio of schools having laboratory those having library?
(a) 1 : 2
(b) 5 : 3
(c) 2 : 1
(d) 2 : 3Â (CAT 1991)

Question 9
(CAT 2001)

Answer: Option 2






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