The equation (M + 6)/36 = (p – 7)/21 relates two temperatu

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Gmat_mission: Legendary Member; Posts: 1622; Joined: Thu Mar 01, 2018 7:22 amFollowed by: 2 members

by Gmat_mission » Sun May 05, 2019 10:49 am

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The equation (M + 6)/36 = (p – 7)/21 relates two temperature scales, where M is the number of degrees on one scale and P is the number of degrees on the other scale. Which of the following equations can be used to convert temperatures from the P scale to the M scale?

(A) M = (12/7)P + 13
(B) M = (12/7)P + 21
(C) M = (12/7)P – 12
(D) M = (12/7)P – 13
(E) M = (12/7)P – 18

[spoiler]OA=E[/spoiler]

Source: GMAT Paper Tests

Source: Beat The GMAT — Problem Solving | Sun May 05, 2019 10:49 am

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Jay@ManhattanReview: GMAT Instructor; Posts: 3008; Joined: Mon Aug 22, 2016 6:19 amFollowed by: 34 members; Location: Grand Central / New York; Thanked: 470 times

by Jay@ManhattanReview » Mon May 06, 2019 12:15 am

Gmat_mission wrote:The equation (M + 6)/36 = (P – 7)/21 relates two temperature scales, where M is the number of degrees on one scale and P is the number of degrees on the other scale. Which of the following equations can be used to convert temperatures from the P scale to the M scale?

(A) M = (12/7)P + 13
(B) M = (12/7)P + 21
(C) M = (12/7)P – 12
(D) M = (12/7)P – 13
(E) M = (12/7)P – 18

[spoiler]OA=E[/spoiler]

Source: GMAT Paper Tests

We are given (M + 6)/36 = (P – 7)/21

Multiplying each side by 3, we have 3*[(M + 6)/36 = (P – 7)/21] => (M + 6)/12 = (P – 7)/7 => 7M + 42 = 12P – 84 => 7M = 12P – 84 – 42 => 7M = 12P – 126 => M = (12/7)P – 126/7 => M = (12/7)P + 18

The correct answer: E

Hope this helps!

-Jay
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GMATGuruNY: GMAT Instructor; Posts: 15539; Joined: Tue May 25, 2010 12:04 pmFollowed by: 1906 members; Location: New York, NY; Thanked: 13060 times; GMAT Score:790

by GMATGuruNY » Mon May 06, 2019 3:30 am

Gmat_mission wrote:The equation (M + 6)/36 = (p – 7)/21 relates two temperature scales, where M is the number of degrees on one scale and P is the number of degrees on the other scale. Which of the following equations can be used to convert temperatures from the P scale to the M scale?

(A) M = (12/7)P + 13
(B) M = (12/7)P + 21
(C) M = (12/7)P – 12
(D) M = (12/7)P – 13
(E) M = (12/7)P – 18
[/spoiler]

Source: GMAT Paper Tests

If M=30 and P=28, both sides of (M + 6)/36 = (P – 7)/21 are equal to 1.
The correct answer must yield a valid equation for M=30 and P=28.
When the question stem includes the phrase "which of the following," the correct answer is likely to be D or E.

E: M = (12/7)P – 18
If M=30 and P=28, we get:
30 = (12/7)(28) - 18
30 = 48-18
30=30
Success!

The correct answer is E.

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Scott@TargetTestPrep: GMAT Instructor; Posts: 8246; Joined: Sat Apr 25, 2015 10:56 amFollowed by: 29 members; Location: Los Angeles, CA; Thanked: 43 times

by Scott@TargetTestPrep » Thu May 09, 2019 5:10 pm

Gmat_mission wrote:The equation (M + 6)/36 = (p – 7)/21 relates two temperature scales, where M is the number of degrees on one scale and P is the number of degrees on the other scale. Which of the following equations can be used to convert temperatures from the P scale to the M scale?

(A) M = (12/7)P + 13
(B) M = (12/7)P + 21
(C) M = (12/7)P – 12
(D) M = (12/7)P – 13
(E) M = (12/7)P – 18

[spoiler]OA=E[/spoiler]

Source: GMAT Paper Tests

We need to isolate M:

(M + 6)/36 = (P - 7)/21

21(M + 6) = 36(P - 7)

7(M + 6) = 12(P - 7)

7M + 42 = 12P - 84

7M = 12P - 126

M = (12/7)P - 18

Answer: E

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