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Difficulty:
35%
(medium)
Question Stats:
70% (01:36) correct
30%
(01:37)
wrong
based on 444
sessions
History
Date
Time
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Not Attempted Yet
Is \(3^p > 2^q\) ?
(1) \(q = 2p\)
(2) \(q > 0\)
_________________
(1) \(q = 2p\)
(2) \(q > 0\)
Pure algebraic questions like this one are no longer part of the GMAT Data Sufficiency syllabus.
For relevant Data Sufficiency questions, please check the Data Sufficiency forum:
Data Sufficiency Forum
Data Sufficiency Forum
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Bunuel
\(3^p > 2^q\) ?
(1) \(q = 2p\)..
\(3^p>2^q.........3^p>2^{2q}..........3^p>4^p\)
if p and q are positive ... NO.....\(3^2>4^2.....9>16\)
if p and q are negative ... YES.....\(3^{-2}>4^{-2}.....\frac{1}{9}>\frac{1}{16}\)
Insuff
(2) \(q > 0\)
Nothing about p
insuff
combined
always NO
suff
C
_________________
raunakd11
Joined: 30 Jan 2020
Last visit: 25 Nov 2020
Posts: 139
Location: India
Schools: ISB YLP 2020 NUS '23
GPA: 4
Schools: ISB YLP 2020 NUS '23
Posts: 139
Bunuel
Hello guys!
Statement 1 says that,
\(q=2p,\)
\(p=\frac{q}{2}\)
Let's plug in numbers, using q=2
3^q/2 > 2^q
3^2/2 > 2^2
3^1> 4
It is not true that 3> 4
Let's plug in one more number for better validation, using q=0
3^q/2 > 2^q
3^0/2> 2^0
3^0>2^0
1>1
It is not true that 1>1
As we did not find a unique solution to this. This statement is not sufficient.
Statement 2 says that,
q>0
This statement alone does not help us, as it does not throw out any numbers.
This statement also is not sufficient.
Let's combine both the statements 1 and 2,
We can be definite on the fact that
3^p> 2^q is not true, which helps us to understand that statements 1 and 2 are sufficient.
Official Answer:- Option C
Thank you!
Regards,
Raunak Damle
Divsri
p and q could be anything. The answer will always be NO.
\(3^p>2^q\)
\(3^{\frac{1}{2}}>2^1\)
\(1.7>2\)….NO
Answer will remain C.
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