If a and b are integers, is b a?

Question

If  a  and  b  are integers, is  b > a ?

(1)  \frac{−30}{b}= a

(2)  (a – b)(a + b) = –11

Are You Up For the Challenge: 700 Level Questions

Fdambro294 · Answer

is b > a? Given that A and B must be integers.

S1:

Can be rearranged to:

A * B = -30

Case 1: A = +5 and B = -6 ——- B < A
NO

Case 2: A = -5 and B = +6——- B> A
YES

S2:

Re-arranged using the difference of squares template:

(A)^2 - (B)^2 = -11

(A)^2 = (B)^2 - 11

25 = 36 - 11

Case 1: A = +5 and B = -6 ——NO

OR

Case 2: A = -5 and B = +6——-YES

Together:

A * B = -30

And

(A)^2 = (B)^2 - 11

Both cases used individually to prove each statement insufficient can be used again to prove both statements together insufficient.

E

Posted from my mobile device

Nipungupta9081 · Answer

IMO E

(1) −30/b = a

-30 = b * a 
-30 can be obtained by -1*30 , -5*6 and -15*2.

A and B doesn't have same values------- INSUFFICIENT

(2) (a–b) (a+b)= –11

A^2 - B^2 = -11.

Still don't know value of A and B . 
it could be -5 or 5 and -6 or 6. ------------- INSUFFICIENT

Combing Both

We don't don't get definite value of A and which proves if B > A.

commodork71 · Answer

I think it's E

From Statement 1, we find that ab=-30. While there area a range of possible values for either, we know that a and b have different signs, i.e. one is positive and one is negative.

From statement 2, multiplying the left side gives us a^2=b^2-11. This means that, while we still don't know the actual values, it must be that |b|>|a|, as b's square is larger.

Combining the two statements, we know that one the two, a and b, is negative and one is positive (neither can be zero per statement 1) and that |b|>|a|. However, we still don't know which is positive and which is negative, and therefore we don't know which is larger than the other.

TarunKumar1234 · Answer

If a and b are integers, is b>a?

Stat1: −30/b=a or, ab= -30; now (a,b) = (2,-15) or (-15,2)....So, Not sufficient to know, if b>a

Stat2: (a–b)(a+b)=–11
Or, a^2- b^2 = -11 or, a= +-5 and b= +-6, So, Not sufficient to know, if b>a

Combining both stats
if a = +5, then b= -6 and b<a but, a=-5, then b=6 and b>a, again Not sufficient

So, I think E.

GCMEMBER · Answer

Is b > a?

(1) −30/b = a

-30 = ab 
Either a or b can be greater. 
Not sufficient

(2) (a–b)(a+b)= –11

a^2 - b^2 = -11.
Either a or b can be greater.
Not sufficient

(1) + (2)

a^2 - b^2 = -11
b^2 - a^2 = 11
And ab = -30

Either a or b can be greater
Not sufficient

Option E

Posted from my mobile device

chetan2u · Answer

(1)  \frac{−30}{b}= a 
 -30=ab=-1*30=-30*1=-6*5  and so on
insuff

(2)  (a – b)(a + b) = –11 
 (a – b)(a + b) = –11=-1*11=-11*1=11*-1=1*-11 
Insuff

Combined
a=-5 and b=6......b>a
a=5 and b=-6....a>b

Insuff

bumpbot · Answer

Automated notice from GMAT Club BumpBot: 

A member just gave Kudos to this thread, showing it’s still useful. I’ve bumped it to the top so more people can benefit. Feel free to add your own questions or solutions.

 This post was generated automatically.

If a and b are integers, is b > a?

Prep Toolkit

Top 5 GMAT Debrief Videos

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards

GMAT Data Sufficiency (DS) Questions