In what year was Ellen born?

Forget conventional ways of solving math questions. In DS, Variable approach is the easiest and quickest way to find the answer without actually solving the problem. Remember equal number of variables and independent equations ensures a solution.

In what year was Ellen born?

(1) Ellen’s brother Pete, who is 1 1/2 years older than Ellen, was born in 1956.
(2) In 1975 Ellen turned 18 years old.


In the original condition, you need to figure out the year Ellen was born. So, there is 1 variable, which should match with the number of equations. So you need 1 equation. For 1) 1 equation, for 2) 1 equation, which is likely to make D the answer.
For 1), since it’s 1/2 from 1 and 1/2 years older, it is not unique and not sufficient. That is, if the older brother Pete was born in December 1956, Ellen should have been born in 1958. If Pete was born in January 1956, Ellen should have been born in 1957.
For 2), it makes Ellen born in 1957 since she turned 18 in 1975, which is unique and sufficient. Therefore, the answer is B.


-> For cases where we need 1 more equation, such as original conditions with “1 variable”, or “2 variables and 1 equation”, or “3 variables and 2 equations”, we have 1 equation each in both 1) and 2). Therefore, there is 59 % chance that D is the answer, while A or B has 38% chance and C or E has 3% chance. Since D is most likely to be the answer using 1) and 2) separately according to DS definition. Obviously there may be cases where the answer is A, B, C or E.

Step 1: Analyse Question Stem

We have to find out the exact year in which Ellen was born.

Step 2: Analyse Statements Independently (And eliminate options) – AD / BCE

Statement 1: Ellen’s brother Pete, who is 1 \(\frac{1}{2}\) years older than Ellen, was born in 1956.

This means that Pete is 18 months older than Ellen.
Pete was born in 1956.

If he was born on the 1st of January 1956, Ellen’s birth year would be 1957 (Do not worry about what his birthday is, if you do that, you are just getting into unnecessary details)

If he was born on the 31st of December 1956, Ellen’s birth year would be 1958

Note that knowing the year and the age difference is not sufficient information to ascertain a unique value for the birth year of Ellen. Those of you who just said that this statement is sufficient did not pay attention to detail.
Attention to detail is something GMAT wants every test taker to pay to every piece of information given in a GMAT question. It also wants you to dig deeper rather than just scratching at the surface for answers.

The data in statement 1 is insufficient to find out a unique value for birth year of Ellen.
Statement 1 alone is insufficient. Answer options A and D can be eliminated.

Statement 2: In 1975 Ellen turned 18 years old.
This can happen only if Ellen was born in the year 1957.

The data in statement 2 is sufficient to find out a unique value for the birth year of Ellen.
Statement 2 alone is sufficient. Answer option C and E can be eliminated.

The correct answer option is B.

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