If a + b − 2c = 12, and 3a + 3b + c = 22, what is the value of c ?

Question

A. −2
B. 0
C. 10
D. 17
E. 34

Archit3110 · Answer

a+b=12+2c
and
3*(a+b)+c=22
so
c=-2
IMO A

KSBGC · Answer

Given ,

a + b - 2c = 12

a + b = 12 + 2c

again

3a + 3b + c = 22

3( a + b) + c = 22

3( 12 + 2c) + c = 22

36 + 6c + c = 22

7c = -14

c = -2.

A is the correct answer.

js17 · Answer

a+b=12+2c
and
3*(a+b)+c=22
so
c=-2

A is correct

Abhishek009 · Answer

a + b − 2c = 12

Or,  3a + 3b − 6c = 36  &  3a + 3b + c = 22

Now,  ( 3a + 3b − 6c ) - ( 3a + 3b + c ) = 36 - 22

Or,  -7c = 14

or,  c = -2 , Answer must be (A)

TheNightKing · Answer

a + b − 2c = 12
3a + 3b + c = 22

3 variables 2 equations obviously mean that we will have to modify equations and cancel the undesired variables.

3(a + b − 2c) = 3(12) becomes 3a+3b-6c=36

So now we have
3a+3b-6c=36
3a + 3b + c = 22

Subtract 2 from 1. We get -7c=14. c=-2.

Option A.

ScottTargetTestPrep · Answer

Multiplying the first equation by -3, we have:

-3a - 3b + 6c = -36

Adding the two equations together, we have:

7c = -14

c = -2

Answer: A

hiranmay · Answer

If a + b − 2c = 12, and 3a + 3b + c = 22, what is the value of c ?

A. −2 -->   correct : a + b − 2c = 12 => a+b = 12+2c; and 3a + 3b + c = 22 => 3(a+b)+c =22, replacing a+b =12+2c, 3*(12+2c) +c =22 => 7c = -14 => c =-2 
B. 0
C. 10
D. 17
E. 34

If a + b − 2c = 12, and 3a + 3b + c = 22, what is the value of c ?

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GMAT Problem Solving (PS) Questions

If a + b − 2c = 12, and 3a + 3b + c = 22, what is the value of c ?

Prep Toolkit

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards