In a certain history class of 17 juniors and seniors, each junior has

Question

In a certain history class of 17 juniors and seniors
First equation :
j+s = 17

Each junior - 2 book reports and each senior - 3 book reports. Total = 44 book reports
Second equation
2j + 3s = 44

Solving first and second equation
s = 10 , j = 7

A. 7
B. 8
C. 9
D. 10
E. 11

PS57330.02

BrentGMATPrepNow · Accepted Answer

STRATEGY : Upon reading any GMAT Problem Solving question, we should always ask,   Can I use the answer choices to my advantage?   
In this case, we can easily test the answer choices. 
Now let's give ourselves up to 20 seconds to identify a faster approach. 
In this case, we can also apply algebra to solve the question. 
I think testing the answer choices will be faster, so I'll go with that....

APPROACH #1: Test the answer choices 
Let's start by testing the middle value, since that may allow us to eliminate other answer choices as well.

C. 9  . This means 9 of the 17 students are juniors, which means the remaining 8 students must be seniors. 
So, in this case, the total number of book reports = (9)(2) + (8)(3) = 18 + 24 = 42
Since we want a total of 44 book reports, answer choice C is incorrect. 
Also, since each senior student writes 1 book report more than each junior student, we must increase the number of senior students in order to reach a total of 44 book reports. 
So, if we want  increase  the number of senior students, we must  decrease  the number of junior students 
In other words, we need fewer than 9 junior students, which means we can also eliminate answer choices D and E.

Let's test answer choice B next. 
 B. 8  . This means 8 of the 17 students are juniors, which means the remaining 9 students must be seniors. 
So, in this case, the total number of book reports = (8)(2) + (9)(3) = 16 + 27 = 43
Since we want a total of 44 book reports, answer choice B is incorrect.

At this point, we can be certain that the correct answer must be A. 
 Answer: A

APPROACH #2: Algebraic approach  
  In a certain history class of 17 juniors and seniors...  
Since the question asks us to find the number of juniors, let's let  x  = the number of juniors in the class
Since there are only juniors and seniors, and since there are 17 students in total, we know that  17 - x  = the number of seniors in the class

Each junior has written  2  book reports and each senior has written  3  book reports. The 17 students have written a total of 44 book reports  
Total number of books written by juniors =  2x 
Total number of books written by seniors =  3(17 - x) 
So we can write:  2x  +  3(17 - x)  = 44
Expand: 2x + 51 - 3x = 44
Simplify: -x + 51 = 44
Solve: x = 7

Answer: A

Cheers,
Brent

nick1816 · Answer

If there were 17 seniors in the class, the number of reports written would be 17*3=51

Actual number of written reports = 44

Number of juniors = (51-44) = 7

GMATinsight · Answer

everyone reads at least 2 book hence total books read = 17*2 = 34

Remaining books to read = 44-34 = 10

i.e. each of these books must be distributed to a senior

SInce we have 10 books left so they would be distributed to 10 seniors

i.e. Juniors = 17-10 = 7

Answer: Option A

nitin942 · Answer

In a certain history class of 17 juniors and seniors 
First equation :
j+s = 17

Each junior - 2 book reports and each senior - 3 book reports. Total = 44 book reports 
Second equation
2j + 3s = 44

Solving first and second equation
s = 10 , j = 7

MHIKER · Answer

J=  Juniours,  S= Seniors

J+S=17

S=17-J

2J+3S=44

2J+3(17-J)=44

2J+51-3J=44

J=7

The answer is  A

Marcost · Answer

2j +3s =44
Analyze each answer choice:

Correct.
A. If j=7; then s=10 ..... 2j+3s=44

Just for save, let’s try the other answers.

B. J=8; s=9 ..... 2j+3s = 43
C. J=9; s=8 ..... 2j+3s = 42
D. J=10; s=7 ..... 2j+3s = 41
E. J=11; s=6 ..... 2j+3s = 40

ThatDudeKnows · Answer

A few different ways to get to the right answer, as articulated in various posts above. But I'm a huge fan of PITA (Plugging in the Answers) and look for opportunities to put it to use whenever possible.

Out of answer choices B, C, and D, which looks easiest to work with (with rare exception, start with B, C, or D since they typically give more information than A and E)?

I'll go with D. 
10 juniors at 2 books each is 20 books. 7 seniors at 3 books each is 21 books. That's 41 total books. Is that what we wanted? Nope. D is wrong.

If you try D and it doesn't work, B is USUALLY the best thing to try second. We will see why in a minute. Okay, so B.
8 juniors at 2 books each is 16 books. 9 seniors at 3 books each is 27 books. That's 43 total books. Is that what we wanted? Nope. B is wrong.

D missed the target by 3 books. B moved in the right direction, but still missed by 1 book. So we need to keep going smaller. Only A is smaller.

Answer choice A.

If D had missed too small and B had missed too large, we'd have known it was C.
If D had missed to small and B had gotten even smaller, we'd have known that we went the wrong direction, so E.

ThatDudeKnowsPITA

Fucio · Answer

Since every senior reads 1 book more than every junior "replacing" one senior with one junior means subtracting one book from the total number of books read.

If there were 17 seniors in the class the total number of books read would be 17*3 = 51, 51-44= 7, it means we need 7 more juniors in place of seniors so the number of juniors is 7 and the number of seniors is 10.

Correct answer: A

In a certain history class of 17 juniors and seniors, each junior has

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