Elmo makes N sandwiches for a fundraiser. For each sandwich he uses B

Question

Elmo makes N sandwiches for a fundraiser. For each sandwich he uses B globs of peanut butter at 4 cents per glob and J blobs of jam at 5 cents per glob. The cost of the peanut butter and jam to make all the sandwiches is 2.53. Assume that B, J and N are all positive integers with N > 1. What is the cost of the jam Elmo uses to make the sandwiches?

(A) 1.05
(B) 1.25
(C) 1.45
(D) 1.65
(E) 1.85

Are You Up For the Challenge: 700 Level Questions

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Official Answer

D

(A) 1.05
(B) 1.25
(C) 1.45
(D) 1.65
(E) 1.85

Are You Up For the Challenge: 700 Level Questions

av1901 · Answer

N,B,J are all positive integers and N >1

N sandwiches, each with B blobs peanut butter  4  cents per blob and J blobs jam @ 5 cents per blob and total cost of 2.53
So the equation should read like (number of sandwiches) times (quantity*cost of raw materials) = total cost:
N * (4B + 5J) = 253 (converted 2.53 to cents)
253 has 4 factors (1,253) and (11,23) and since both N and (4B + 5J) are greater than 1, we can safely assume that
N * (4B + 5J) = 11*23

Now, we need to figure out which of the 2 is 11 and which is 23
The question tells us that N, B and J are all positive integers and 4B + 5J in no integer combination can give us 11 so N =1 and the other expression is 23

4B + 5J = 23 which implies that B = 2 and J = 3 (only possible integer set that will satisfy the equation)

Now, we need to find the total cost of jam for all sandwiches = N * 5J = 11*5*3 = 165 cents or 1.65 dollars

Answer - D

SaquibHGMATWhiz · Answer

This is a question related to something we call a "special equation".

Cost of jam = 5J cents and cost of peanut butter = 4B
Since the total cost is $2.53 so we can say 4B + 5J = 253 (converting in terms of cents)
Now since 253 is the cost of N sandwiches so we can say N must be a factor of 253 
Since N is greater than 1 so the possible factors are 11, 23, 253
Now if N = 253, then 4B + 5J = 1 which does not make sense as J and B are integers
So we can say N = 11 or N 23

If N = 11,
 
4B +5J = 23
We can do hit and trial here however we should know the proper approach as well (Specially keeping DS in mind),
Or, 4B = 23 - 5J
Or, 4B = 20 - 4J + 3 - J
 Now, here $B is a multiple of 4 and thus the right-hand side must be a multiple of 4 and hence we must have J = 3
Note, that 20 and 4J are already multiples of 4 so 3 - J must be a multiple of 4
J = 3 would mean B = 2

If N = 23,
 
  4B + 5J = 11
Or, 4B = 11 - 5J
or, 4B = 8 - 4J + 3 - J so here also J = 3.
 But J = 3 would mean B is - 1 and that is not possible and hence only one possible solution is there.

Thus the total cost = N × 5 × J = 11 × 5 × 3 = 165 cents or $1.65

The answer is option D.

GMATGuruNY · Answer

Let B = the total number of peanut butter globs and J = the total number of jam globs.

Since B globs of peanut butter are used to make N sandwiches, the number of peanut butter globs per sandwich =  \frac{B}{N} 
Since J globs of jam are used to make N sandwiches, the number of jam globs per sandwich =   \frac{J}{N} 
Implication:
B and J must both be divisible by N.

Since the total cost of the 4-cent peanut butter globs and 5-cent jam globs is 235 cents, we get:
4B+5J=235

We can PLUG IN THE ANSWERS, which represent the total cost of the jam (5J).
When the correct answer is plugged in, B and J will both be divisible by N.

B: 5J = 125 --> J=25
Since 4B+5J=253 and 5J=125, 4B=128 --> B=32
J=25 and B=32 have no factors in common other than 1.
Thus, this answer choice does not yield a viable option for N.
Eliminate B.

D: 5J = 165 --> J=33
Since 4B+5J=253 and 5J=165, 4B=88 --> B=22
J=33 and B=22 are both divisible by 11.
Thus:
N=11, implying that 11 sandwiches are made with J=33 globs of jam and B=22 globs of peanut butter.
Success!

D

Wadree · Answer

Cost of all sandwich = $ 2.53 = 253 ¢ 
If he she makes N sandwich....each cost same .... then...N ×   = 253 ¢
So...N is a factor of 253 ......now there are only 4 factors of 253..... 1, 11, 23 and 253....but N ≠ 1, 253 .......
So...N must be 11....or 23 .... But...if she makes 23 sandwich...then each will cost = 11 ¢ ......but peanut butter glob worth 4 ¢ ... and jam glob worth 5 ¢ ...... and....   +   ≠ 11 .....
So.....she must've made 11 sandwich....then each cost 23 ¢ ...... and....23 =   +   .....so it matches.....
So....cost of jam in 1 sandwich = 3 × 5 = 15 ¢ ......so..... cost of jam in 11 sandwich = 11 × 15 = 165 ¢ = 1.65 $

! nah id win!

Elmo makes N sandwiches for a fundraiser. For each sandwich he uses B

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Elmo makes N sandwiches for a fundraiser. For each sandwich he uses B

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