Good Quant. Questions for CAT

Q1. The number of two-digit numbers [Where neither digit is zero] whose product of the digits is a square are?
a. 16                   b. 17                 c. 18                  d. None of these

Q2. What is a percent of b divided by b percent of a?
(a) a        (b)b           (c)    1    (d)10           (e)    100

Q3. There are four boys and five girls standing outside the new record shop. The sign in the window offers a prize to every couple (one boy and one girl) that enters the store. How many prizes can the nine people get?

Q4. While taking a class Sirji asked
“What is the highest number possible with 3 digits?”
My answer then was 9 to the 99th power (written mathematically of course) as this uses “3 digits” and is obviously a huge number. Is this correct?
a. yes        
b. no        
c. cant be determined            
d. There is not a single highest number

Q5. Among 39 sequential natural numbers there always is a number with the sum of its digits divisible by
I. 11           II. 13            III. 17
a. only I
b. Both I & II
c. I, II & III
d. None of the above