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12 May 2021, 06:30
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A
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Difficulty:
65%
(hard)
Question Stats:
48% (02:00) correct
52%
(01:58)
wrong
based on 44
sessions
History
Date
Time
Result
Not Attempted Yet
If n and m are integers, and \(x=3^n\), and \(y=3^m\), is the value of x greater than the value of 2y?
(1) \(n=m+1\)
(2) \(n=2m\)
(1) \(n=m+1\)
(2) \(n=2m\)
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:
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12 May 2021, 08:16
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1.) Plugging in n = m+1 into x=3^n gives 3^m+1 which can be changed to x= 3^m * 3 SUFFICIENT
2.) Plugging in n = 2m into x=3^n gives x=3^2m which can be changed to x = 3^m * 3^m while y = 3^m
plugging in 1, 0 and -1 in for my gives:
1: x=9 y=3 x>y
0: x=1 y=1 x=y
-1: x= 1/9 y= 1/3 x<y
INSUFFICIENT
Answer A
2.) Plugging in n = 2m into x=3^n gives x=3^2m which can be changed to x = 3^m * 3^m while y = 3^m
plugging in 1, 0 and -1 in for my gives:
1: x=9 y=3 x>y
0: x=1 y=1 x=y
-1: x= 1/9 y= 1/3 x<y
INSUFFICIENT
Answer A
12 May 2021, 08:55
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Asked: If n and m are integers, and \(x=3^n\), and \(y=3^m\), is the value of x greater than the value of 2y?
(1) \(n=m+1\)
\(x = 3^n = 3^{m+1} = 3*3^m = 3y\)
x = 3y > 2y when y > 0
But x = 3y < 2y when y < 0
NOT SUFFICIENT
(2) \(n=2m\)
\(x = 3^n = 3^{2m}= (3^m)^2 = y^2\)
x = y^2 > 2y when y>2 or y<0
But x = y^2 < 2y when 0<y<2 or y=1
NOT SUFFICIENT
(1) + (2)
(1) \(n=m+1\)
(2) \(n=2m\)
n = m + 1 = 2m
m = 1
n = 2
\(x = 3^2 = 9\)
\(y = 3^1 =3\)
x = 9 > 2y = 6
SUFFICIENT
IMO C
(1) \(n=m+1\)
\(x = 3^n = 3^{m+1} = 3*3^m = 3y\)
x = 3y > 2y when y > 0
But x = 3y < 2y when y < 0
NOT SUFFICIENT
(2) \(n=2m\)
\(x = 3^n = 3^{2m}= (3^m)^2 = y^2\)
x = y^2 > 2y when y>2 or y<0
But x = y^2 < 2y when 0<y<2 or y=1
NOT SUFFICIENT
(1) + (2)
(1) \(n=m+1\)
(2) \(n=2m\)
n = m + 1 = 2m
m = 1
n = 2
\(x = 3^2 = 9\)
\(y = 3^1 =3\)
x = 9 > 2y = 6
SUFFICIENT
IMO C
