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

I think it is B
We have b > 1.2 a
b> 70 ?
(1) b-a=20
b = a + 20 > 1.2 a
a < 100 => not sufficient
(2) a > 70
b > 1.2 a > 1.2 * 70 > 70 => sufficient

Please correct me if I am wrong. Thanks

Statement 1, b-a = 20

Assume a=10 b=30, meets both the original condition and the one given in the statement. b<70
Assume a=60 b=80, meets both the original condition and the one given in the statement. B>70
Two solutions, so insufficient.

Statement 2, a>70
Since A>70, b which is greater than 120% of a is also greater than 70
So ans is B

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.
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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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