amanvermagmat wrote:

In a history class of a humanities course, there are N students present on a particular day. If N is a two digit number, then what is the value of N?

(1) If 2 more students had been present in the class, they could have been evenly divided in groups of 5 each.

(2) If 2 less students had been present in the class, they could have been evenly divided in groups of 7 each.

We'll translate our statements into equations so we understand what we need to do.

This is a Precise approach.

We need to solve for N.

(1) This tells us that N + 2 = 5k, that is, it is divisible by 5. Selecting k = 1 or k = 2 give different values of N.

Insufficient.

(2) This tells us that N - 2 = 7p, that is, it is divisible by 7. Similarly to the above, this is insufficient.

Insufficient.

Combined:

We know have two equations: N+2=5k and N-2=7p

Subtracting the second from the first gives 4=5k-7p. We know that both k and p are integers so we can cycle through the different options.

We'll cycle through values of 'p' as there are less of them.

If p=1 --> 5k=11. Impossible.

If p=2 we add 7 to the above --> 5k=11+7=18. Impossible.

p=3 --> 5k = 18+7 = 25 --> k=5. In this case N = 23

p=4 --> 5k = 25+7 = 32. Impossible.

p=5 --> 5k = 32+7 = 39. Impossible.

p=6 --> 5k = 39+7 = 46. Impossible.

p = 7--> 5k = 46+7 = 53. Impossible.

p = 8 --> 5k = 53+7 = 60 ---> k = 12. In this case N = 58.

Then (Combined) is still insufficient.

(E) is our answer.

_________________

Sign up for 7-day free trial