If Sam were twice as old as he is, he would be 40 years older than Jim

Question

If Sam were twice as old as he is, he would be 40 years older than Jim. If Jim is 10 years younger than Sam, how old is Sam?

A. 20
B. 30
C. 40
D. 50
E. 60

CounterSniper · Answer

2S=40+J -----1
J=S-10 -------2

substituting 2 in 1

2J+20 = 40 + J
J=20
S=30

ritu1009 · Answer

Ans is B
Let Sam present age is x
So Jim age=2x-40
Also Jim age= x-10
Therefore x-10=2x-40
 x=30

Shruti0805 · Answer

Hi, As per the question, Jim is younger than Sam but the highlighted expression implies Sam is 10 years younger than Jim. It should be J = S-10 . Same issue with the final values you've calculated as well - Jim's age has turned out to be 10 years more than Sam's

ScottTargetTestPrep · Answer

We can let the current age of Sam and Jim = S and J, respectively, and create the equations:

2S = J + 40

and

J = S - 10

Substituting, we have:

2S = S - 10 + 40

S = 30

Answer: B

EMPOWERMathExpert · Answer

Let  x  be Sam’s age and let  y be Jim’s age. We can now translate the following phrases into algebraic expressions:
 
  “Twice Sam’s age is 40 years greater than Jim’s age.“  
 
 2 	imes \ Sam’s \ age = Jim’s \ age + 40 
 
  2x = y + 40

“Jim’s age is 10 years less than Sam’s age.“  
 Jim’s \ age \ = Sam’s \ age – 10 
  y = x – 10

We can now solve the system of equations using substitution.

2x = y + 40 
 
Replace  y  with  (x – 10) :
 
 2x =    (x – 10)    + 40 
 2x = x + 30 
 x = 30

Therefore, Sam is 30 years old. The final answer is  B .

BrentGMATPrepNow · Answer

Jim is 10 years younger than Sam  
Let x = Sam's PRESENT age
So,  x - 10  = Jim's PRESENT age

If Sam were twice as old as he is, he would be 40 years older than Jim.   
TWICE Sam's age = 2x
So, we can write: 2x = ( x - 10 ) + 40
Simplify: 2x = x + 30
Solve: x = 30

Answer: B

Cheers,
Brent

EMPOWERgmatRichC · Answer

Hi All,

We're told that if Sam were TWICE as old as he is, then he would be 40 years older than Jim and that Jim is currently 10 years YOUNGER than Sam. We're asked for Sam's current age. This question can be solved in a couple of different ways, including by TESTing THE ANSWERS. Since the difference between the two ages is currently 10 years, and the answer choices are in increasing increments of 10 years, it's likely that we're dealing with one of the smaller answers (since by DOUBLING Sam's age will only increase the difference to 40 years). Let's TEST Answer B first:

Answer B: 30 years

IF... Sam is 30 years old 
Jim is 30 - 10 = 20 years old 
Doubling Sam's age.... (2)(30) = 60 years 
60 - 20 = 40 years difference. 
This matches everything that we were told, so this must be the answer.

Final Answer:  B

GMAT assassins aren't born, they're made, 
Rich

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If Sam were twice as old as he is, he would be 40 years older than Jim

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If Sam were twice as old as he is, he would be 40 years older than Jim

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