If the sum of five integers is 875, what is the product of these

Question

If the sum of five integers is 875, what is the product of these integers?

(1) The integers are consecutive.

(2) All the integers are positive.

M10-03

Bunuel · Answer

If the sum of five integers is 875, what is the product of these integers? 
 
(1) The integers are consecutive.
 
Express the sum of these integers as:  (x-2)+(x-1)+x+(x+1)+(x+2)=875 . This equation simplifies to  5x=875 . From this, we can determine the value of  x , and therefore get all five integers as well as their product. Sufficient.
 
Alternatively, it can be observed that there is only one set of five consecutive integers that sum to 875. Thus, the sequence is uniquely determined, and each term can be identified.
 
(2) All the integers are positive.
 
Clearly insufficient.

Answer: A

sidinsin · Answer

HI
For St A:
We could have the numbers as: (x)+(x+1)+(x+2)+(x+3)+(x+4)+(x+5)=875 or (x-2)+(x-1)+x+(x+1)+(x+2)=875. In either case, the value of X will be different.
 For St B:
Not Suff

A+B: Not Suff

Thus, IMO the answer should be E

Bunuel · Answer

No, that's not correct.

First of all, it should be (x)+(x+1)+(x+2)+(x+3)+(x+4)=875 (we have 5 terms not 6) --> x =  173 .

Next, notice that x in my solution is the third term while in yours it's the first. From my solution x=175, so the first term is  173 . As you can see the sequence is the same in both cases: {173, 174, 175, 176, 177}.

You will get the same result if you denote the 5th, or any other term by x.

Anyway, you could avoid all this calculations if you understand the second approach given there: there can be only one set of five consecutive integers which add up to 875, so the sequence is fixed and thus its each term can be found.

Hope it's clear.

pierjoejoe · Answer

can we use sequences here?

we know that the sum of a sequence is

( /2)*n

we know that n = 5 and the sum is 875. thus to know the product we need to know d.

(1) consecutive integers have d = 1 --> sufficient to find a(1) and thus all the other values for the product. S
(2) does not give us any info NS

If the sum of five integers is 875, what is the product of these

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GMAT Data Sufficiency (DS) Questions

If the sum of five integers is 875, what is the product of these

Prep Toolkit

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