If 0 < x < y and x and y are Consecutive Perfect Squares GMAT Data Sufficiency

bySayantani Barman Experta en el extranjero

Question: If 0 < x < y and x and y are consecutive perfect squares, what is the remainder when y id divided by x?

Both x and y have 3 positive factors
Both \(\sqrt{x} and \sqrt{y}\) are prime numbers

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

Answer:
Solution with Explanation:
Approach Solution (1):

Notice that since x and y is consecutive perfect squares, and then \(\sqrt{x} and \sqrt{y}\) are consecutive integers

(1) Both x and y have 3 positive factors. This statement implies that x = \((prime_1)^2\)and y =.\((prime_2)^2\)

From above we have that \(\sqrt {x} = (prime_1) \) and \(\sqrt {y} = (prime_2) \)are consecutive integers. The only two consecutive integers which are prime are 2 and 3
Thus, x = \((prime_1)^2\) = 4 and y = \((prime_2)^2\) = 9
The remainder when 9 is divided by 4 is 1
Sufficient

(2) Both \(\sqrt{x} and \sqrt{y}\) are prime numbers. The same here: \(\sqrt{x} = 2 , \sqrt{x} = 3\)

Sufficient

Correct Option: D

Approach Solution (2):

It seems that you are missing the crucial part the stem tells us: x and y are consecutive perfect squares. So, for example:

\(1^2 and 2^2 ;\)
\(2^2 and 3^2;\)
\(3^2 and 4^2;\)
...

So, if x and y are consecutive perfect squares, then \(\sqrt{x} and \sqrt{y}\) are consecutive integers:
1 and 2;
2 and 3;
3 and 4;
…

Both statements imply that \(\sqrt{x} and \sqrt{y}\) are primes. The only two consecutive integers which are primes are 2 and 3.

Correct Option: D

Approach Solution (3):

x and y are consecutive perfect squares, so x and y could be:
x = 1 and y = 4 — sqrt (x) = 1 and sqrt (y) = 2, consecutive integers;
x = 4 and y = 9 — sqrt (x) = 2 and sqrt (y) = 3, consecutive integers;
x = 9 and y = 16 — sqrt (x) = 3 and sqrt (y) = 4, consecutive integers;

S1 is sufficient and S2 is sufficient

Correct Option: D

“If 0 < x < y and x and y are consecutive perfect squares, what is the remainder when y id divided by x?”- is a topic of the GMAT Quantitative reasoning section of GMAT. This question has been taken from the book "GMAT Quantitative Review". 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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If 0 < x < y and x and y are Consecutive Perfect Squares GMAT Data Sufficiency

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