If Bob's Age is Three Times David's Age, What is Bob's Age? GMAT Data Sufficiency

Question: If Bob's age is three times David's age, what is Bob's age?

(1) Two years ago, Bob age was exactly 5 times David's age.
(2) Twelve years from now, Bob'b age will be exactly 50% greater than David's age.

1. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
2. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.
3. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
4. EACH statement ALONE is sufficient.
5. Statements (1) and (2) TOGETHER are not sufficient.

Correct Answer: D
Solution and Explanation:
Approach Solution 1:
According to the question, Bob is three times as old as David.

Statement 1 Alone says
Bob was exactly five times David’s age, two years ago.

This can be shown in the following way.

If we assume the age of Bob to be b,
And the age of David to be d,

Therefore, according to the statement, we see
That, Bob, is three times David’s age.
b= 3d

Now if we take the first statement alone, where we see that it has been said,

Two years ago, Bob was five times the age of David. So we get,
b-2 = 5(d-2)
b-2 = 5d -10.
b= 5d -8

Thus, b= 3d (2)

Now, suppose
d= 4

Therefore, b = 20, from the above equation.
Hence, Statement 1 alone is SUFFICIENT

Statement 2 alone
In statement 2, we have

Twelve years from now, Bob’s age will be exactly 50% greater than David's age.
This can be proven in the following way,

We know, that twelve years hence, Bob’s age will be b+12, and David’s age will be d+12
Therefore, according to the question,
That Bob’s age will be 50% of David’s age
Therefore, 50% of 3= 1.5,

Thus,
b+12 = 1.5 (d+12)
b + 12 = 1.5d + 18
b = 1.5d + 6 = 3d (3)
d = 6/1.5 = 4
b = 20

Thus, Statement 2 alone is SUFFICIENT for the answer.
Therefore, each of the sentences is alone sufficient

Approach Solution 2:
Bob is three times as old as David. This information is given in the question.

We are to find the age of Bob.
First take the first of the two sentences given below the question, which says

Bob was exactly five times David’s age, two years ago.

Statement 1 Alone says
Bob was exactly five times David’s age, two years ago.
This can be shown in the following way.

Here we need to make some assumptions.
If we assume the age of Bob to be X,
And the age of David to be Y,

Therefore, according to the statement, we see
Bob is three times David’s age.
X=3Y

Now if we take the first statement alone, where we see that it has been said,
Two years ago, Bob was five times the age of David. So we get,
X-2 = 5(Y-2)
X-2 = 5Y -10.
X= 5Y -8
Thus, X= 3Y (2)

So, we get
Y= 4

Therefore, X = 20, from the above equation.
Hence, Statement 1 Alone is SUFFICIENT

Now we are taking the second statement Alone.

Statement 2 alone
In statement 2, we have
Twelve years from now, Bob’s age will be exactly 50% greater than David's age.
This can be proven in the following way,

We know, that twelve years hence,
Bob’s age will be b+12, and David’s age will be d+12
Therefore, according to the question,
That Bob’s age will be 50% of David’s age

Therefore, 50% of 3= 1.5,

Therefore,
X+12 = 1.5 (Y+12)
X + 12 = 1.5Y + 18
X = 1.5Y + 6
X= 3Y (3)

Y = 6/1.5 = 4
X = 20

Thus, Statement 2 alone is SUFFICIENT for the answer.
Therefore, both sentences are alone sufficient for the answer.

Approach Solution 3:
According to the question, Bob is three times as old as David.

Which means,
Bob’s age = 3 * David’s age.
We are asked to find the age of Bob.

The two statements given below are,

Statement 1: Two years ago, Bob’s age was exactly 5 times David's age.
Statement 2: Twelve years from now, Bob's age will be exactly 50% greater than David's age.

Now, if we take the first statement separately,

Statement 1 Alone says
Bob was exactly five times David’s age, two years ago.
This can be shown in the following way.
If we assume the age of Bob to be m,
And the age of David to be n,

Therefore, according to the statement, we see
Bob is three times David’s age.
m=3n

Now if we take the first statement alone, where we see that it has been said,
Two years ago, Bob was five times the age of David.

Two years ago,
Bob’s age will be m-2,
David’s age will be n-2,

Thus we get,
m-2 = 5(n-2)

Therefore, there are two variables m and n, and two equations
Thus, the value of m can be easily found.
m-2 = 5n-10.
m= 5n -8

We know, m= 3n (2)

Therefore we get
n = 4,

Therefore, m = 20, from the above equation.
Hence, Statement 1 alone is SUFFICIENT

Now, if we take Statement 2 alone

In statement 2, we have
Twelve years from now, Bob’s age will be exactly 50% greater than David's age.
This can be proven in the following way,
We know, that twelve years hence, Bob’s age will be m+12, and David’s age will be n+12

Therefore, according to the question,
There are two variables m and n, and two equations
Thus, the value of m can be easily found.
m+12 = 1.5 (n+12)
m + 12 = 1.5n+ 18
m= 1.5n + 6

We also have, m= 3n

Thus, we can take,
1.5n+6=3n

Therefore, n = 6/1.5 = 4
m = 20

Hence, Statement 2 alone is SUFFICIENT for the answer.
Therefore, each of the sentences is alone sufficient

“If Bob's age is three times David's age, what is Bob's age?”- is a topic of the GMAT Quantitative reasoning section of GMAT. GMAT Quant section consists of a total of 31 questions. GMAT Data Sufficiency questions consist of a problem statement followed by two factual statements. GMAT data sufficiency comprises 15 questions which are two-fifths of the total 31 GMAT quant questions.

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