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If a and b are integers, and |a| > |b|, is a |b| < a

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If a and b are integers, and |a| > |b|, is a |b| < a [#permalink] New post 17 Mar 2011, 09:49
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E

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If a and b are integers, and |a| > |b|, is a · |b| < a – b?

(1) a < 0

(2) ab >= 0
[Reveal] Spoiler: OA

Last edited by n2739178 on 18 Mar 2011, 03:20, edited 1 time in total.
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Re: How to solve quickly!?!? [#permalink] New post 17 Mar 2011, 12:28
There is no sign in (2) so i could not sell anything about it.

Regarding (1):
It is obviously not enough.
Assume that b is 0 and a is -1. Then the inequality is 0<-1 which is false
Assume that b is -1 and a is -2. Then the inequality is -2<-1 which is true

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Re: How to solve quickly!?!? [#permalink] New post 17 Mar 2011, 18:00
You dont need to know the sign dood. You have the official answer, which is E.

Therefore the sign must have been ab <0.

(If it was ab>0 then we would know that both a and b are positive integers. This would be enough information to know that the above inequality is always incorrect).

Therefore we know that a is +ve integer, b is -ve integer. Unfortunately this information does not let us solve it, and to solve this quickly we just plug in numbers.

A=5, B=-2.... 10>7
A=5, B=-1.....5<6. We dont know from both so E, quickly move on.
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Re: How to solve quickly!?!? [#permalink] New post 17 Mar 2011, 21:39
From 1, a < 0

Now a is -ve, and b can be -ve or +ve

if a = -2, -1 <= b <= 1

-2 *|-1| < -2 -(-1)

-2 < -1

But -2.|1| > -2 - (1) because -2 > -3, so (1) is insufficient


If ab < 0 then they have opposite signs, hence the same problem as above:

Combining (1) and (2), not sufficient, b > 0, but :


if a = -1, b = 6

a * |b| = -6 > -7

if a = -1 b = 1

a*|b| = -1 > -2

So answer is E.

@bostonrb, I think you might want to take -ve values of A and prove it ?

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Re: How to solve quickly!?!? [#permalink] New post 17 Mar 2011, 21:43
Btw, I searched for this and in MGMAT forum it is suggested that the symbol is ab >= 0 and the answer is still E.

http://www.manhattangmat.com/forums/if- ... t9437.html

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Re: How to solve quickly!?!? [#permalink] New post 17 Mar 2011, 22:06
Yeah subhash, I misread (1) as saying that a is +ve, hence everything I wrote is for that case.. (why I always get a couple questions wrong in Q =/)

If we take ab>=0 as per the link, and a<0, then a is -ve, b is 0 or -ve.

choose a=-5. is -5 |b|<-5-b ??? For any neg integer b, RHS will at least be -4 while LHS will at most be -5. Therefore it would be (C).. only b can be 0! In that case it doesnt stand, 0 is not <a (as per statement 1), so the possibility of b=0 makes it (E).

Last edited by bostonrb on 18 Mar 2011, 04:06, edited 1 time in total.
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Re: How to solve quickly!?!? [#permalink] New post 18 Mar 2011, 03:20
forgot to put the operator in statement 2... amended. apologies!

(2) ab >= 0
Re: How to solve quickly!?!?   [#permalink] 18 Mar 2011, 03:20
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