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

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If a/b > 4, is a > 8?  [#permalink]

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New post Updated on: 03 Dec 2013, 00:56


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

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

Originally posted by wastedyouth on 02 Dec 2013, 10:35.
Last edited by Bunuel on 03 Dec 2013, 00:56, edited 1 time in total.
Renamed the topic, edited the question and added the OA.
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Re: if a/b>4  [#permalink]

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New post 02 Dec 2013, 11:43
wastedyouth wrote:
If a/b>4 . is a>8?

1) b>2.
2) a>7

Dear wastedyouth,
I'm happy to help with this. :-)

Here's a blog about DS questions with inequalities: ... qualities/

In this question, we are given that (a/b) > 4, and then we are asked: is a > 8?

Statement #1: b > 2
Well, we know that
a = (a/b)*b
Well, if the first factor, (a/b) is greater than 4, and the second factor, b, is greater than 2, then the product of something greater than 4 and something greater than 2 has to be greater than 8. Thus, a must be greater than 8. This statement allows us to give a definitive answer to the prompt. This statement, alone and by itself, is sufficient.

Statement #2: a > 7
This doesn't involve b at all, so the fraction is irrelevant. We are left with --- if we know a > 7, then is it true that a > 8? Well, of course, it could be true: there are plenty of numbers greater than both 7 & 8 -----e.g. 9, 10, 11, 12, etc. BUT, it might not be true. For example, if a = 8, then a is greater than 7 but not greater than 8. Furthermore, nothing in the problem specifies that a & b are integers --- they are general numbers, so we have to keep our minds open to all categories of numbers. It turns out there is a continuous infinity of decimals greater than 7 and less than 8 --- the decimals in that single step of the number line outnumber all the atoms in the Universe! Any one of that infinity of values could be the value of a, in which case a would be greater than 7 but less than 8. Thus, we can find values of a that satisfy this statement and yet answer the prompt question either way. This statement does not determine a definitive answer. This statement, alone and by itself, is insufficient.

Answer = (A)

Does all this make sense?
Mike :-)

Mike McGarry
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Re: if a/b>4  [#permalink]

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New post 02 Dec 2013, 22:26
wastedyouth wrote:
If a/b>4 . is a>8?

1) b>2.
2) a>7

From the given Q stem we can say that a/b -4 >0 or

(a- 4b)/ b >0 ---------> 1

From St1 we have b>2 ie. b>0 therefore on multiplying both sides of the inequality by b will not change the sign and we get

a-4b>0 or a>4b....Now if b = 2.0001 then a > 8.0004 or greater then 8
b = 3 then a> 12.

Hence for any value of b> 2. A will be greater than 8

So option B,C and E ruled out

from st 2 we have a>7

let a = 7.6 then if b =1.8 then

(7.6-7.2)/1.8 >0 yes

but if a =7.6 and b = 1.9 then

(7.6- 1.9*4)/1.9 = 0 and not greater than 0 as per the given Q stem.

Hence D ruled out.

Ans A

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Re: If a/b > 4, is a > 8?  [#permalink]

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New post 03 Dec 2013, 00:59
If a/b > 4, is a > 8?

(1) b > 2. Since b is positive, then from the stem we have that a > 4b (we can multiply by b both sides). Now, since given that b > 2, then 4b > 8, therefore a > 4b > 8. Sufficient.

(2) a > 7. If a = 7.5 and b = 1 (a/b > 4), then a < 8 but if a = 10 and b = 1 (a/b > 4), then a > 8. Two different answers. Not sufficient.

Answer: A.

Hope it's clear.

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Re: If a/b > 4, is a > 8?  [#permalink]

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