Is b^2 ≤ a^2 (1) b ≤ a (2) a + b = a − b

Question

Is  b^2≤a^2

(1)  b ≤ a

(2)  a+b = a−b

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GMATinsight · Answer

Please find below the video explanation of the question

Answer: Option B

https://www.youtube.com/watch?v=4GwDqn89bMs

eakabuah · Answer

We are to determine if  b^2≤a^2

Statement 1:  b≤a 
Statement 1 is insufficient. When  a=3  and  b=2 , then the answer is No. However, when  b=-2  and  a=-1  satisfying statement 1,  b^2=4  while  a^2=1  and the answer is Yes.

Statement 2:  a+b=a-b 
Sufficient since we know that  b=0  from statement 2. Irrespective of the value of  a ,  b^2≤a^2.

The answer is therefore B.

GMATWhizTeam · Answer

Solution Step 1: Analyse Question Stem Is b^2 ≤ a^2 ? Step 2: Analyse Statements Independently (And eliminate options) – AD/BCE Statement 1: b ≤ a • Case I: If a= 2 and b= 1, a^2 = 4 and b^2 = 1 o Then, b^2 ≤ a^2 • Case II: If a = 2 and b = -3, then a^2 = 4 and b^2 = 9 o Then b^2 > a^2 • We are getting different results. Hence, statement 1 is not sufficient, we can eliminate the answer options A and D. Statement 2: a + b = a- b • a -a = -b -b • 0 = -2b o b = 0 o Case 1: If a =0, then a^2 = b^2 o Case 2: If a < 0, then a^2 will always be a positive number o 0 < a^2, b^2 < a^2 o Case 3: If a > 0, then a^2 will always be a positive number o 0 < a^2, b^2 < a^2 o We can say that, b^2 ≤ a^2 Hence, statement 2 is also sufficient, the correct answer is Option B

Kinshook · Answer

Asked: Is  b^2≤a^2

(1)  b ≤ a 
If b=-2; a=1; b<a but b^2 = 4>a^2 = 1
But if b=1; a = 2; b<a and b^2 = 1<a^2 = 4
NOT SUFFICIENT

(2)  a+b = a−b 
b = 0
b^2 = 0 <= a^2 for any value of a
SUFFICIENT

IMO B

lacktutor · Answer

Is  b^2 ≤ a^2  ?
-->  (a-b)(a+b) ≤0  ???

( Statement1 ):  b ≤ a 
-->  b-a ≤0  
Since nothing tells us about what  a  and  b  are,  (b+a)  could be positive or negative.
 Insufficient

( Statement2 ):  a+b =a−b 
-->  2b =0   -->  b=0 
 a  could be negative, zero or positive number

Case1: a=-5, b =0 
--->  0^{2} ≤ (-5)^{2}  (YES)

Case2: a=0, b =0 
--->  0^{2} ≤ 0^{2}  (YES)

Case3: a=5, b =0
--->  0^{2} ≤ (5)^{2}  (YES)

Sufficient

Answer (B).

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Is b^2 ≤ a^2 (1) b ≤ a (2) a + b = a − b

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