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

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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

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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

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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

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

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