Is the product of positive integers x and y a prime number?

Question

(1) x/y = prime
(2) x and y are consecutive integers

CrackverbalGMAT · Answer

Question: Is the product of x and y a prime number.

Constraint: x and y are positive integers i.e x,y ≠ 0

This is a Yes/No type of DS question, and we should try to put in values to get to the answer.

Statement 1:   x/y = prime

If x = 2 and y = 1, then x/y = 2/1 = 2 which is prime and x * y = 2 * 1 = 2, which is a prime number.

If x = 4 and y = 2, then x/y = 4/2 = 2 which is prime and x * y = 4 * 2 = 8, which is not a prime number.

Therefore Statement 1 Alone is Insufficient  . Answer options could be B, C or E.

Statement 2:   x and y are consecutive integers

if x = 1 and y = 2, then x * y = 2 which is a prime number.

if x = 2 and y = 3, then x * y = 6 which is not a prime number.

Therefore Statement 2 Alone is Insufficient  . Answer options could be C or E

Combining Both Statements:

x and y are consecutive integers and x/y is prime.

This is satisfied only when x = 1 and y = 2 as for all other consecutive numbers, we will not get integer values.

Therefore x * y = 1 * 2 = 2 which is a prime number

Therefore Both Statements together are Sufficient  .

Option C

Arun Kumar

QuantMadeEasy · Answer

Step 1: understanding statement 1 alone 
(1) x/y = prime
When x = 2, y =1; x/y = 2; xy = 2
When x = 4, y = 2; x/y = 2; xy = 8
Insufficient

Step 2: Understanding statement 2 alone  
(2) x and y are consecutive integers
When x = 2, y =1; xy = 2
When x = 3, y =2; xy = 6
Insufficient

Step 3: Combining (1) and (2) 
As x and y are consecutive integers and x/y is prime, x=2, y=1; xy = 2
Sufficient

IMO C

MathRevolution · Answer

Forget the conventional way to solve DS questions.

We will solve this DS question using the variable approach.

DS question with 2 variables: Let the original condition in a DS question contain 2 variables. Now, 2 variables would generally require 2 equations for us to be able to solve for the value of the variable.

We know that each condition would usually give us an equation, and Since we need 2 equations to match the numbers of variables and equations in the original condition, the logical answer is C.

To master the Variable Approach, visit https://www.mathrevolution.com and check our lessons and proven techniques to score high in DS questions.

Let’s apply the 3 steps suggested previously. [Watch lessons on our website to master these 3 steps]

Step 1 of the Variable Approach: Modifying and rechecking the original condition and the question.

We have to find 'Is the product of x and y a prime number' - where 'x' and 'y' are positive integers.

Second and the third step of Variable Approach: From the original condition, we have 2 variables (x and y). To match the number of variables with the number of equations, we need 2 equations. Since conditions (1) and (2) will provide 2 equations, C would most likely be the answer.

Let’s take look at both the conditions combined together.

Condition(1) tells us that x /y = prime.

Condition(2) tells us that 'x' and 'y' are consecutive integers.

=> For x = 2 and y = 1: 2 / 1 is prime and x * y = 2 * 1 is prime - YES product of positive integers x and y is a prime number

Since the answer is unique YES , both conditions combined together are sufficient by CMT 1.

Both conditions combined together are sufficient.

So, C is the correct answer.

Answer: C

SAVE TIME: By Variable Approach, when you know that there are two variables and you need 2 equations, mark your likely answer as C.

IanStewart · Answer

Statement 1 here does not give you an "equation".

Basshead · Answer

Is the product of positive integers x and y a prime number?

(1) x/y = prime

4/2 = prime. 4 * 2 = not prime
2/1 = prime. 2 * 1 = prime

INSUFFICIENT.

(2) x and y are consecutive integers

1 * 2 = prime
2 * 3 = not prime

INSUFFICIENT.

(1&2) x = 1 y = 2. SUFFICIENT.

Answer is C.

Is the product of positive integers x and y a prime number?

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GMAT Data Sufficiency (DS) Questions

Is the product of positive integers x and y a prime number?

Prep Toolkit

615 to 715 in 15 Days (Ria's Strategies)

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