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.
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