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# The sum of the heights of two high-rises is x feet. If the first high

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Math Expert
Joined: 02 Sep 2009
Posts: 53020
The sum of the heights of two high-rises is x feet. If the first high  [#permalink]

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30 Jan 2015, 06:36
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Difficulty:

15% (low)

Question Stats:

85% (02:15) correct 15% (02:44) wrong based on 66 sessions

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The sum of the heights of two high-rises is x feet. If the first high rise is 37 feet taller than the second, how tall will the second high rise be after they add an antenna with a height of z feet to the top?

A. (x+z)/2 + 37
B. 2x−(37+z)
C. (x−37)/2 + z
D. x/2 - 37 + z
E. (2x−37)/z

Kudos for a correct solution.

The OA will be revealed on Sunday

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Re: The sum of the heights of two high-rises is x feet. If the first high  [#permalink]

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30 Jan 2015, 08:12
Hello Bunuel, I gave it a try:

I will note h1 the height of high-rise 1 and h2 the height of high-rise 2. SO:

h1 + h2 = x
and h1 = h2 + 37 =>

Q: h2 + z = ?

h2 + h2 + 37 = x => 2h2 = x-37 =? h2 = (x-37)/2

=> h2 + z = (x-37)/2 + z, CORRECT ANSWER C

Bunuel wrote:
The sum of the heights of two high-rises is x feet. If the first high rise is 37 feet taller than the second, how tall will the second high rise be after they add an antenna with a height of z feet to the top?

A. (x+z)/2 + 37
B. 2x−(37+z)
C. (x−37)/2 + z
D. x/2 - 37 + z
E. (2x−37)/z

Kudos for a correct solution.

The OA will be revealed on Sunday

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Posts: 7334
Re: The sum of the heights of two high-rises is x feet. If the first high  [#permalink]

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30 Jan 2015, 08:13
ans C..
let the smaller be y , higher will be y+37... so y+y+37=x or y=(x-37)/2..
now z is added on y...therefore height will be y+z or (x-37)/2+z
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Re: The sum of the heights of two high-rises is x feet. If the first high  [#permalink]

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30 Jan 2015, 09:23
1
Lets assume taller h1 and the shorter high is h2:

As problem says h1+h2=x & h1=h2+37,

We replace these two relations in the equation and we have h2+h2+37=x OR : 2h2+37=x and after adding z to the x , we have 2h2+37=x

Or : 2h2= x-37 and finally we get :h2= (x-37)/2+z

so the shorter h2 is (x-37)/2 +z answer c
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Re: The sum of the heights of two high-rises is x feet. If the first high  [#permalink]

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31 Jan 2015, 01:14
1
Bunuel wrote:
The sum of the heights of two high-rises is x feet. If the first high rise is 37 feet taller than the second, how tall will the second high rise be after they add an antenna with a height of z feet to the top?

A. (x+z)/2 + 37
B. 2x−(37+z)
C. (x−37)/2 + z
D. x/2 - 37 + z
E. (2x−37)/z

Kudos for a correct solution.

The OA will be revealed on Sunday

call height_1 H, call height_2 K.

H+K=x ---> 2K+37=x ---> K=x-37/2 add the antenna and you get answer C
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Re: The sum of the heights of two high-rises is x feet. If the first high  [#permalink]

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02 Feb 2015, 03:39
Bunuel wrote:
The sum of the heights of two high-rises is x feet. If the first high rise is 37 feet taller than the second, how tall will the second high rise be after they add an antenna with a height of z feet to the top?

A. (x+z)/2 + 37
B. 2x−(37+z)
C. (x−37)/2 + z
D. x/2 - 37 + z
E. (2x−37)/z

Kudos for a correct solution.

The OA will be revealed on Sunday

VERITAS PREP OFFICIAL SOLUTION:

If F is the height of the first building and S is the initial height of the second, we know from the problem that: F + S = x and F = S + 37 By substituting the second equation into the first we get: (S + 37) + S = x; solving for S gives, S = (x−37)/2.

Adding an antenna to the second building will give it a total (new) height of S + z = (x−37)/2 + z

The correct answer is C.
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The sum of the heights of two high-rises is x feet. If the first high  [#permalink]

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29 Dec 2017, 10:42
Bunuel wrote:
The sum of the heights of two high-rises is x feet. If the first high rise is 37 feet taller than the second, how tall will the second high rise be after they add an antenna with a height of z feet to the top?

A. (x+z)/2 + 37
B. 2x−(37+z)
C. (x−37)/2 + z
D. x/2 - 37 + z
E. (2x−37)/z

Kudos for a correct solution.

The OA will be revealed on Sunday

let b+z=height of second building with antenna
x=2b+37➡
2b=x-37➡
b=(x-37)/2
b+z=(x-37)/2+z
C
The sum of the heights of two high-rises is x feet. If the first high   [#permalink] 29 Dec 2017, 10:42
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# The sum of the heights of two high-rises is x feet. If the first high

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