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GRE Math Challenge #64-If x, y, and z represent
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03 May 2015, 01:19
03 May 2015, 01:19
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Question Stats:
84% (00:38) correct
16% (00:51) wrong based on 25 sessions
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If x, y, and z represent consecutive integers, and x < y < z, which of the following equals y?
I. x + 1
II. (x + z)/2
III. (x + y + z)/3
A. I only
B. I and II only
C. I and III only
D. II and III only
E. I, II and III
I. x + 1
II. (x + z)/2
III. (x + y + z)/3
A. I only
B. I and II only
C. I and III only
D. II and III only
E. I, II and III
Retired Moderator
Joined: 10 Apr 2015
Posts: 6218
Given Kudos: 136
Re: GRE Math Challenge #64-If x, y, and z represent
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23 Oct 2018, 06:57
23 Oct 2018, 06:57
1
sandy wrote:
If x, y, and z represent consecutive integers, and x < y < z, which of the following equals y?
I. x + 1
II. (x + z)/2
III. (x + y + z)/3
A. I only
B. I and II only
C. I and III only
D. II and III only
E. I, II and III
I. x + 1
II. (x + z)/2
III. (x + y + z)/3
A. I only
B. I and II only
C. I and III only
D. II and III only
E. I, II and III
If x, y, and z represent consecutive integers, and x < y < z, then we can write:
x = x
y = x + 1 (since y must be 1 greater than x)
z = x + 2 (since z must be 1 greater than y)
Now check the 3 statements....
I. x + 1
Perfect! We can be certain that y = x + 1
Statement I works
II. (x + z)/2
Take: (x + z)/2
Replace z with x + 2 to get: (x + x + 2)/2
Simplify numerator to get: (2x + 2)/2
Divide numerator and denominator by 2 to get: (x + 1)/1, which equals x + 1
Perfect!
Statement II works
III. (x + y + z)/3
Take: (x + y + z)/3
Replace y with x+1 and replace z with x+2 to get: (x + x+1 + x+2)/3
Simplify numerator to get: (3x + 3)/3
Divide numerator and denominator by 3 to get: (x + 1)/1, which equals x + 1
Perfect!
Statement III works
Answer: E
Cheers,
Brent
gmatclubot
Re: GRE Math Challenge #64-If x, y, and z represent [#permalink]
23 Oct 2018, 06:57
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