In a history class of a humanities course, there are N students

Question

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.

DavidTutorexamPAL · Answer

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.

GMAT215 · Answer

it is clear that A & B are not sufficient. solving them together: Considering statement 1 : we have all the digits from 1 to 99 that has unit digit of 3 or 8 ,, only then adding two will be evenly divisible by 5. now, Considering statement 2, keeping in mind that the number must be ending with 3 or 8 : 7 14 21 28 35 42 49 56 63 70 77 84 91 98 9 16 23 30 37 44 51 58 65 72 79 86 93 100 more than one solution hence, not sufficient. kudoss, if it helped.

aserghe1 · Answer

Statement 1
 N + 2 = 5k  -->  N = 5k - 2  where  k  is an integer
Make a quick list of possible values of N:
{13, 18, 23, 28 etc}
Not sufficient

Statement 2
 N - 2 = 7p  -->  N = 7p + 2  where  p  is an integer
Make a quick list of possible values of N:
{16, 23, 30, etc}
Not sufficient

Combine 1 & 2
Per statement 1, N can be {13, 18, 23, 28 etc}
Per statement 2, N can be {16, 23, 30, etc}
Note that the first term in common is 23. The next term in common will be: 23 + LCM(5,7) = 23 + 35 = 58
More than 2 values of N are possible.
Not sufficient

Answer: E

AkshdeepS · Answer

St 1: N + 2 = 5k , Or N = 5k - 2 -------- (I) Insufficient as we have no info about N and k

N can be 3, 8, 13, 18, 23 etc

St 2: N - 2 = 7k , Or N = 7k + 2 -------(II) Insufficient as we have no info about N and k

N can be 9, 16, 23, 30 etc

We need to check to for some other values with formula : (LCM of 5 & 7) + (first common value)

35k + 23 : - common values are 23, 58, 93 etc.

Insufficient

(E)

bumpbot · Answer

Automated notice from GMAT Club BumpBot: 

A member just gave Kudos to this thread, showing it’s still useful. I’ve bumped it to the top so more people can benefit. Feel free to add your own questions or solutions.

 This post was generated automatically.

In a history class of a humanities course, there are N students

Prep Toolkit

Top 5 GMAT Debrief Videos

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards

GMAT Data Sufficiency (DS) Questions

In a history class of a humanities course, there are N students

Prep Toolkit

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards