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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  [#permalink]

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New post 17 Sep 2018, 23:13
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If Sam were twice as old as he is, he would be 40 years older than Jim  [#permalink]

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New post Updated on: 18 Sep 2018, 00:19
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Bunuel wrote:
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


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

substituting 2 in 1

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

Originally posted by CounterSniper on 17 Sep 2018, 23:41.
Last edited by CounterSniper on 18 Sep 2018, 00:19, edited 2 times in total.
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If Sam were twice as old as he is, he would be 40 years older than Jim  [#permalink]

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New post Updated on: 18 Sep 2018, 02:41
Bunuel wrote:
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



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

Originally posted by ritu1009 on 17 Sep 2018, 23:53.
Last edited by ritu1009 on 18 Sep 2018, 02:41, edited 1 time in total.
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Re: If Sam were twice as old as he is, he would be 40 years older than Jim  [#permalink]

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New post 18 Sep 2018, 00:11
1
CounterSniper wrote:
Bunuel wrote:
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


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

substituting 2 in 1

2J-20 = 40 + J
J=60
S=50



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 :)
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Re: If Sam were twice as old as he is, he would be 40 years older than Jim  [#permalink]

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New post 23 Sep 2018, 16:38
Bunuel wrote:
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



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
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Re: If Sam were twice as old as he is, he would be 40 years older than Jim  [#permalink]

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New post 27 Sep 2018, 00:57
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.“

\(2 \times \ Sam’s \ age = Jim’s \ age + 40\)

\(2x = y + 40\)

“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 .
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Re: If Sam were twice as old as he is, he would be 40 years older than Jim  [#permalink]

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New post 19 Jan 2019, 09:56
Top Contributor
Bunuel wrote:
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


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
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Re: If Sam were twice as old as he is, he would be 40 years older than Jim  [#permalink]

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New post 20 Jan 2019, 13:51
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:

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Re: If Sam were twice as old as he is, he would be 40 years older than Jim   [#permalink] 20 Jan 2019, 13:51
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