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Manager
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If s, u, and v are positive integers, and 2^s = 2^u + 2^v, [#permalink]
 19 Mar 2006, 16:26
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If s, u, and v are positive integers, and 2^s = 2^u + 2^v, which of the following must be true:
1: s=u
2: u does not equal v
3: s > v
A) None
B) I only
C) II only
D) III only
E) II and III only
Please explain your answers.
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VP
Joined: 29 Dec 2005
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[quote="jcgoodchild"]If s, u, and v are positive integers, and 2^s = 2^u + 2^v, which of the following must be true:
i. s=u....... not possible cuz even if v is o or -ve, s must be > u.
ii. u does not equal v ............ not true. if s = 3, u=v=2. so not true.
iii. s > v. it is a must cuz even if either u or v is -ve, s must be > v.
so D is correct.
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Manager
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jcgoodchild wrote: If s, u, and v are positive integers, and 2^s = 2^u + 2^v, which of the following must be true:
1: s=u
2: u does not equal v
3: s > v
A) None
B) I only
C) II only
D) III only
E) II and III only
Please explain your answers.
for 1:
s,u,v > 0
therefore v > = 1 thus
s cannot be equal to u
for 2:
is actually the opposite for s,u,v > 0 and integers u does always equal v
for 3:
s,u,v > 0
from 2 we know that U=V then s>v
so I would say D
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GMAT Club Legend
Joined: 07 Jul 2004
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1) Not true.
If s = u, then v must be 0 which cannot be the case since v must be a positive integer.
2) Not true.
u and v can be equal. If s = 3, u and v = 2
3) True
If s, u and v are positive integers, then s must always be greater than v.
I go with D
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