M13 Q 32

Question

Is  a^b \gt b^a  ?

1.  a \gt b \gt 1 
 2.  a = b + 1

* Statement (1) ALONE is sufficient, but Statement (2) ALONE is not sufficient
 * Statement (2) ALONE is sufficient, but Statement (1) ALONE is not sufficient
 * BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient
 * EACH statement ALONE is sufficient
 * Statements (1) and (2) TOGETHER are NOT sufficient

Ans (E)

Can someone please provide suitable set of numbers for testing these statements? I used number testing approach but had a hard time coming up with the right set of numbers? How do you figure what type of numbers should you be testing for these types of questions?

Bunuel · Answer

On DS questions when plugging numbers, your  goal is to prove that the statement is not sufficient . So you should try to get an YES answer with one chosen number(s) and a NO with another.

Is  a^b \gt b^a  ?

(1)  a \gt b \gt 1  --> first try minimum possible integers for  a  and  b : if  a=3  and  b=2  then  a^b=9>8=b^a  and the answer is YES. Now, increase  a  and  b  and try:  a=4  and  b=3  then  a^b=64<81=b^a , so in this case the answer is NO.

(2)  a = b + 1 . The same set of numbers works for this statement as well. Not sufficient.

(1)+(2) Again, two sets of numbers considered, satisfy both statements and give different answer to the question. Not sufficient.

Hope it's clear.

teal · Answer

Thanks a lot, Bunuel!

M13 Q 32

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