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If \(3x – 5 = x + 11\), then \(x =\)
(A) 16
(B) 8
(C) 3
(D) 2
(E) 1
(A) 16
(B) 8
(C) 3
(D) 2
(E) 1
Source: Master GMAT
15 Dec 2019, 21:14
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3x – 5 = x + 11
3x-x= 11+5
2x= 16
x= 8
Answer B
3x-x= 11+5
2x= 16
x= 8
Answer B
SajjadAhmad
If \(3x – 5 = x + 11\), then \(x =\)
(A) 16
(B) 8
(C) 3
(D) 2
(E) 1
(A) 16
(B) 8
(C) 3
(D) 2
(E) 1
Source: Master GMAT
17 Dec 2019, 00:32
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This is a very easy question on a simple linear equation. The traditional method of solving this question is to collect all the variables onto one side, all the constants on the other and then simplify using mathematical operations.
However, since this is a very simple question, let’s try and see how we can use the back-solving strategy to solve it.
Starting with option C, let’s say x=3. Substituting this in the equation given, we have LHS = 3*3-5 = 4 and RHS = 3+11 = 14. Clearly, LHS ≠ RHS. So, x cannot be 3. From this, we can also realise that the LHS is much smaller than the RHS, so taking smaller values for x will only make the LHS smaller than the RHS again.
This lets us eliminate answer options C, D and E. Moving to answer option B – substituting x = 8, LHS = 3*8 – 5 = 19 and RHS = 8 + 11 = 19. LHS = RHS. Should we try answer option A also? Clearly not because we have a LINEAR equation on hand and a linear equation can only have ONE solution because its degree is ONE. We have already found that one solution and hence there is no need to worry about A being able to satisfy the equation.
The correct answer option is B.
Hope that helps!
However, since this is a very simple question, let’s try and see how we can use the back-solving strategy to solve it.
Starting with option C, let’s say x=3. Substituting this in the equation given, we have LHS = 3*3-5 = 4 and RHS = 3+11 = 14. Clearly, LHS ≠ RHS. So, x cannot be 3. From this, we can also realise that the LHS is much smaller than the RHS, so taking smaller values for x will only make the LHS smaller than the RHS again.
This lets us eliminate answer options C, D and E. Moving to answer option B – substituting x = 8, LHS = 3*8 – 5 = 19 and RHS = 8 + 11 = 19. LHS = RHS. Should we try answer option A also? Clearly not because we have a LINEAR equation on hand and a linear equation can only have ONE solution because its degree is ONE. We have already found that one solution and hence there is no need to worry about A being able to satisfy the equation.
The correct answer option is B.
Hope that helps!
