If a/b > 4, is a > 8?

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VJesus12: Legendary Member; Posts: 2276; Joined: Sat Oct 14, 2017 6:10 amFollowed by: 3 members

by VJesus12 » Sun Apr 14, 2019 9:46 am

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If a/b > 4, is a > 8?

(1) b > 2
(2) a > 7

[spoiler]OA=A[/spoiler]

Source: Princeton Review

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Source: Beat The GMAT — Data Sufficiency | Sun Apr 14, 2019 9:46 am

Vincen: Legendary Member; Posts: 2898; Joined: Thu Sep 07, 2017 2:49 pmFollowed by: 5 members; Thanked: 6 times

by Vincen » Sat Apr 20, 2019 5:15 am

If a/b > 4, is a > 8?

(1) b > 2
(2) a > 7

[spoiler]OA=A[/spoiler]

Source: Princeton Review

Hi Vjesus12.

We need to answer the question: is a > 8?

Statement 1:

(1) b > 2

If b > 2 and a/b > 4 then we have that $$b\cdot\frac{a}{b}>4\cdot b\ \ >4\cdot2\ \Rightarrow\ \ a\ >8.$$ Hence, the answer is YES. So this statement is SUFFICIENT.

Statement 2:

(2) a > 7

Let's take a look at the following cases:

(i) if a=7.5 and b=1.5 then we have that $ \frac{7.5}{1.5} = 5 > 4$ and $ a < 8$. Here the answer is NO.
(ii) if a=9 and b=2 then we have that $ \frac{9}{2} = 4.5 > 4$ and $ a > 9$. Here the answer is YES.

Since we've got two different answers, we conclude that this statement is NOT SUFFICIENT.

So, the correct answer is the option _A_.

Hope it helps.

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