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

(1) The integers are consecutive integers --> write the sum of these integers as: (x-2)+(x-1)+x+(x+1)+(x+2)=875 --> 5x=875 --> we can find x, hence we can find all five integers and thus their product. Sufficient.

Alternately you could spot that 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.

(2) All five integers are positive. Clearly insufficient.

Answer: A.

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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.
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PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


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