If a and b are positive integers is a

Question

If a and b are positive integers is a < 20 < b < 30?

(1) ab = 22

(2) a^2 < 81 < b^2

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chetan2u · Answer

OA is wrong .. it should be E and not A..
(1) ab=22..
a=1, b=22....yes a<20<b<30
But b=22 and a=1 , ans is no, OR a=2, b=11..no

(2)  a^2<81<b^2...a<9<b 
a=1, b=22... YES
a=2, b=11...NO

Combined..
Same set of Numbers still exists..

E

TarunTilokani · Answer

I agree with you  chetan2u . Even i was getting E as an answer but the official answer stated was A. Couldn't understand why A was right so I posted on the forum.

Salsanousi · Answer

From statement 1)

ab = 22 this would mean a could be 1 and b is 22 or vice versa or a is 2 and b is 11 etc.. since we get different answers it is insufficient.

Statement 2)

a < 9 < b

a satisfies the condition that it is less than 20, but b could be anything including 31 so it is insufficient.

Now if we combine both.

a could be 1,2,11,22 from statement 1)
b could be 1,2,11,22 from statement 1)

Now if a < 9 then it could be 1 or 2

if it is 1 then b is 22 as a result this provides an answer of yes

a = 1 < 20 < b = 22 < 30 , yes

However, if a is 2 then b is 11

a = 2 < 20 < b = 11 < 30 , no.

Since we get two answers then the answer choice is E.

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Archit3110 · Answer

#1
22; 22*1 or 2*11
so relation a < 20 < b < 30 is both yes and no
insufficient
#2
a^2 < 81 < b^2
again a=1 ,b =11
or a=2, b=10
insufficient
IMO E

CrackverbalGMAT · Answer

A fairly simple question on Numbers, this is a question which tests your knowledge of properties of numbers. Be careful not to assume that a<2020. So we get a NO as an answer. In the second case, a<209. Although a<20, we cannot say whether b will always be between 20 and 30. Statement II is insufficient. Answer option B can be eliminated. When we combine the two statements, we have, a = 2 and b = 11 & a = 1 and b = 22. In both the cases, a^2 <81< b^2 . We saw earlier that, when we used these values, we got a YES and NO situation. Clearly, that won’t change now and the combination of statements is still insufficient. The correct answer option is E. Hope this helps!

Shorub · Answer

Spoiler also indicates OA is E.

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If a and b are positive integers is a < 20 < b < 30?

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GMAT Data Sufficiency (DS) Questions

If a and b are positive integers is a < 20 < b < 30?

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