Is the positive integer x an even number? (1) If x is divid

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GMATinsight: Legendary Member; Posts: 1100; Joined: Sat May 10, 2014 11:34 pm; Location: New Delhi, India; Thanked: 205 times; Followed by:24 members

Is the positive integer x an even number? (1) If x is divid

by GMATinsight » Thu Oct 08, 2015 1:38 am

Is the positive integer x an even number?

(1) If x is divided by 3, the remainder is 2.
(2) If x is divided by 5, the remainder is 2.

Answer: option E

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Source: Beat The GMAT — Data Sufficiency | Thu Oct 08, 2015 1:38 am

GMATinsight: Legendary Member; Posts: 1100; Joined: Sat May 10, 2014 11:34 pm; Location: New Delhi, India; Thanked: 205 times; Followed by:24 members

by GMATinsight » Thu Oct 08, 2015 1:39 am

GMATinsight wrote:Is the positive integer x an even number?

(1) If x is divided by 3, the remainder is 2.
(2) If x is divided by 5, the remainder is 2.

Answer: option E

Question : Is the positive integer x an even number?

Statement 1: If x is divided by 3, the remainder is 2.
i.e. x = 3a+2 (Possible values of x = 5, 8, 11, 14, 17, 20, 23, 26, 29...etc.)
@a = Even, x = even+2 = Even
@a = Odd, x = Odd+2 = Odd. Hence,
NOT SUFFICIENT

Statement 2: If x is divided by 5, the remainder is 2.
i.e. x = 5b+2 (Possible values of x = 7, 12, 17, 22, 27, 32, 37...etc.)
@b = Even, x = even+2 = Even
@b = Odd, x = Odd+2 = Odd. Hence,
NOT SUFFICIENT

Combining the two statements
Statement 1 says (Possible values of x = 5, 8, 11, 14, 17, 20, 23, 26, 29, 32, 35, 38...etc.)
Statement 2 says (Possible values of x = 7, 12, 17, 22, 27, 32, 37...etc.)

i.e. x may still be 17, 37, 52, 67... etc. i.e. x may still be Even as well as odd. Hence,
NOT SUFFICIENT

Answer: Option E

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by Scott@TargetTestPrep » Tue Dec 12, 2017 10:07 am

GMATinsight wrote:Is the positive integer x an even number?

(1) If x is divided by 3, the remainder is 2.
(2) If x is divided by 5, the remainder is 2.

We need to determine whether x is an even number.

Statement One Alone:

If x is divided by 3, the remainder is 2.

Statement one alone is not sufficient to answer the question. For example, x could be 5, which is an odd number, or x could be 8, which is an even number.

Statement Two Alone:

If x is divided by 5, the remainder is 2.

Statement two alone is not sufficient to answer the question. For example, x could be 7, which is an odd number, or x could be 12, which is an even number.

Statements One and Two Together:

Using the statements together, we see that the first number that fulfills both statements is n = 2, which is an even number.

To determine the next value in the list, we can use the least common multiple of 3 and 5, which is 3 x 5 = 15. Thus, the next number that could be x is 2 + (5 x 3) = 17, which is an odd number. Thus, the two statements together are still not sufficient to answer the question.

Answer: E

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