a,b, c are three integers such that a

Question

a,b, c  are three integers such that  a<b<c . Is c greater than  a+b ?
1)  ab  is negative
2)  a+b  is negative

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RusskiyLev · Answer

Let us analyze each statement separately: 
 Statement 1 : 
1) ab is negative 
If ab is negative, then either a or b is negative. Since a < b, we can conclude that a is negative. Also it means that b is positive. As a is negative, then a + b < b. 
As b < c, then it is obvious that a + b < c
Sufficient.

Statement 2 
2) a + b is negative 
If a + b is negative, it means that a is negative and the absolute value of a is greater than absolute value of b as a < b.
If both a and b are negative numbers, then their sum would be even smaller than each of numbers individually, so a + b < c
If a is negative, and b is positive, the sum of the two will be less than b, but more than a. 
Anyway, it will be less than c 
a + b < c
Sufficient.

Both statements separately are sufficient to solve the question.

Answer:  D

CrackverbalGMAT · Answer

This question could have been made infinitely more difficult had a<b<c not been given. So, a<b<c is actually a huge piece of data, as you’ll see eventually when we test the statements, added to the fact that a, b and c are integers.

From the question data, we can make out that the biggest number is c and the smallest number is a. Also, knowing that all three numbers are integers actually reduces a lot of our workload because we do not have to worry about fractions/ decimals now.

From statement I , ab < 0. Coupled with a<b<c, we can say that a<0 and b>0. Let’s test a few values here:

If a = -1, b = 1 and c = 2, then c>a+b.

If a = -10, b = 1 and c = 2, then c>a+b.

If a = -100, b = 50 and c = 51, then c>a+b.

As you see, we have tried all sorts of values from one extreme to the other extreme. In all cases, we see that c is always greater than a+b.

Statement I alone is sufficient. Possible answer options are A or D. Answer options B, C and E can be ruled out.

From statement II, a+b<0. Knowing a<b<c and a+b<0, a simple test we could do is this:

If a = -3, b = -2 and c = -1, c>a+b.

If a = -10, b = 9 and c = 10, c>a+b.

Again, c>a+b whatever values we take. Statement II alone is sufficient.

The correct answer option is D.

Using values looks like a sensible approach in this question. Especially, when the question data makes life easy for us by stating that the variables are integers. Had this not been stated, then, drawing up a number line and using absolute values would have been the better approach.

So, always decide your approach, especially in DS questions, based on the kind of data given in the question statement and the two statements which provide data. Do not stick to one approach all the time.

Hope this helps!

a,b, c are three integers such that a<b<c. Is c greater than

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