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10 Nov 2022, 02:30
Kudos
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A
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
65%
(hard)
Question Stats:
32% (01:35) correct
68%
(01:41)
wrong
based on 47
sessions
History
Date
Time
Result
Not Attempted Yet
Is 3^x > 9^y ?
(1) x = 2y + 2
(2) x = 3y
(1) x = 2y + 2
(2) x = 3y
10 Nov 2022, 03:07
Kudos
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Is\( 3^x > 9^y\) ?
We can reframe the question as \( 3^x > 3^{2y}\)
As the base is same the question essentially wants us to find if x > 2y
Statement 1
(1) x = 2y + 2
This statement tells us that x lies 2 units right to 2y on a number line. Hence x will always be greater than 2y.
The statement is sufficient and we can eliminate B, C and E.
(2) x = 3y
On a number line, we know x is thrice as far from 0 than y is. We want to know if the value of x is greater than 2y.
Now if y is positive, the answer will be Yes.
If y is negative, the answer will be No.
To visualize this on a number line, lets take the below two cases -
Case 1
-------3Y-------2Y--------------Y-------0--------------
Case 2
-------0-------Y--------------2Y-------3Y-------
X lies at the position marked in red, while the reference position is marked in green.
As this statement is not sufficient, we can eliminate D.
IMO A
We can reframe the question as \( 3^x > 3^{2y}\)
As the base is same the question essentially wants us to find if x > 2y
Statement 1
(1) x = 2y + 2
This statement tells us that x lies 2 units right to 2y on a number line. Hence x will always be greater than 2y.
The statement is sufficient and we can eliminate B, C and E.
(2) x = 3y
On a number line, we know x is thrice as far from 0 than y is. We want to know if the value of x is greater than 2y.
Now if y is positive, the answer will be Yes.
If y is negative, the answer will be No.
To visualize this on a number line, lets take the below two cases -
Case 1
-------3Y-------2Y--------------Y-------0--------------
Case 2
-------0-------Y--------------2Y-------3Y-------
X lies at the position marked in red, while the reference position is marked in green.
As this statement is not sufficient, we can eliminate D.
IMO A
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