If b is greater than 120 percent of a, is b greater than 70? (1) b – a

Given,
b> 1.2a
implies b-a> 0.2a

Statement 1:
b-a=20
Thus 20> 0.2a
a<100
Thus b<120
NOT SUFFCIENT

Statement 2
a>70
b>a (because b>1.2a)
Thus, b>70

Answer:B

OFFICIAL SOLUTION:

This data sufficiency problem concerns percentages. The problem tells you that b > 1.2a, and it asks you to determine whether b is greater than 70. So you have to find out something about the value of a.

Statement (1) tells you that there’s a difference of 20 between a and b. Being told that b – a = 20 and that b > 1.2a doesn’t provide conclusive data to state that b > 70. For example, a = 10 and b = 30 satisfies both conditions but doesn’t result in b > 70; a = 60 and b = 80 satisfies both conditions and does result in b > 70. Statement (1) isn’t sufficient to answer the question, so the answer is B, C, or E.

Statement (2) tells you that a > 70. If a is greater than 70, then b is greater than 120 percent of 70 (which, of course, is greater than 70). So given statement (2), b is greater than 70. Statement (2) is sufficient; eliminate C and E.

Your answer is B.

The problem tells b>1.2a, is b>70?

1) b-a=20 => b=20+a

20+a > 1.2a => a<100. Putting values arbitarily, we can see b may or may not be > 70. INSUFFICIENT.

2) a>70. Obviously 1.2a will be greater than 70. Thus b is also greater than 70. SUFFICIENT

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