In this article certain questions have been randomly taken from different topics of the quantitative section of CAT. Each question has been selected keeping in mind certain challenges you need to manage as a test taker. These challenges may range from concept basics to application orientation and test taking strategies.

If k is composite than its prime factors are contained in (k-1)!

Hence the question simply translates into finding the number of prime numbers between 20 and 40, which are : 23, 29, 31 and 37.

Hence the question simply translates into finding the number of prime numbers between 20 and 40, which are : 23, 29, 31 and 37.

3. 15

If the total is 8 then the final result will be 13. If it is 9, then the final result will be 13 or 14 with an equal chance of each. If it is 10, then the final result will be 13,14 or 15 with an equal chance of each. If it is 11, then the final result will be 13,14, 15 or 16 with an equal chance of each. If it is 12, then the final result will be 13,14, 15 or 16 with an equal chance of each.

The most likely final result is 13.

The most likely final result is 13.

So we have to check the divisibility of 111…..upto 6/12/18 etc digits by 7 and 11.

It is known that a number of the form xyzxyz is divisible by 1001.

1001= 7*11*13

Thus the given number will be divisible by both 7 and 11

It is known that a number of the form xyzxyz is divisible by 1001.

1001= 7*11*13

Thus the given number will be divisible by both 7 and 11

Let A+C+E = x and B+D+F = y, then

x – y = 11k and x + y= 16

K can’t be 1 or more; if k=1 then x=8.5 which is not possible, and if it is 2 then the value of y comes out to be negative which is not possible. Higher values of k are visibly ruled out. Hence k = 0

Thus x-y=0 or x= y and from x+y=16, we get x=y=8

A, C, E will be 6,2,0 or 4,3,1 and B, D, F will be 4,3,1 or 6,2,0 respectively. Thus A+B= 4+6 or 6+4 =10.

x – y = 11k and x + y= 16

K can’t be 1 or more; if k=1 then x=8.5 which is not possible, and if it is 2 then the value of y comes out to be negative which is not possible. Higher values of k are visibly ruled out. Hence k = 0

Thus x-y=0 or x= y and from x+y=16, we get x=y=8

A, C, E will be 6,2,0 or 4,3,1 and B, D, F will be 4,3,1 or 6,2,0 respectively. Thus A+B= 4+6 or 6+4 =10.

If they meet after 30 s, then l/(m-n)=30 or (m-n)/l=1/30

Let l/m=x and l/n=y. Thus 1/y – 1/x =5 and x-y=1/30

or xy = 1/150. Now (x-y)^{2}= x^{2}+y^{2}-2xy or x^{2}+y^{2}= 13/900

(x+y)^{2}= x^{2}+y^{2}+2xy or x+y= 6 or l/(m+n)= 6 seconds =1/10 minutes.

Thus they will meet 10 times in minute.

Let l/m=x and l/n=y. Thus 1/y – 1/x =5 and x-y=1/30

or xy = 1/150. Now (x-y)

(x+y)

Thus they will meet 10 times in minute.