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What is the remainder when the positive integer x is divided by 2?
(l) x is an odd integer.
(2) x is a multiple of 3.
 

x is a positive integer. we are looking for the remainder when x is divided by 2.

Statement 1: x is odd. odd = 2k + 1 . Remainder will always be 1.

Statement 2: x is a multiple of 3. x = 3, 6 , 9. when x is 3 , remainder is 1. when x is 6 remainder is 0.

The best answer is A.
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Statement 1: x is odd, whenever a positive odd integer is divided by 2, 1 is remainder.... Sufficient
Statement 2: x is multiple of 3, lets suppose, x = 3, 6, 9, 12... When divided by 2, remainder can be 1 or 0... Not Sufficient

Answer = A
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Quote:
What is the remainder when the positive integer x is divided by 2?

Test using numbers when the minimum restriction is given in question stem.
Given: x is positive integer i.e. 1,2, 3 ..

Quote:
(1) x is an odd integer.
Every odd number will always have a remainder of 1 when divided by 2.
Suff

Quote:
(2) x is a multiple of 3.
Pick no.
Say 3 , When divided by 2, remainder is 1
Say 6 , When divided by 2, remainder is 0

Two different values of the remainder , not suff.

OA: A
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I understand the solution to this for the most part except in one case. If 1 is selected for the first "Fact"/"rule", then this gives a remainder of 0 when divided by 2 but 1 is an odd number. So this proves inconsistent because I do agree that all other odd numbers will give a remainder of 1.

Can someone please clarify?

Thanks!
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Hii

Definition of Remainder. : The remainder is the integer "left over" after dividing one integer by another to produce an integer quotient (integer division)

When 1 is divided by 2, the remainder is not zero, remainder is 1.

1 = 2*0 +1, 1 is the remainder.

For example


Attachment:
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viravb
I understand the solution to this for the most part except in one case. If 1 is selected for the first "Fact"/"rule", then this gives a remainder of 0 when divided by 2 but 1 is an odd number. So this proves inconsistent because I do agree that all other odd numbers will give a remainder of 1.

Can someone please clarify?

Thanks!
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GMATBusters

Project DS Butler: Day 2: Data Sufficiency (DS4)


For DS butler Questions Click Here

What is the remainder when the positive integer x is divided by 2?

(1) x is an odd integer.
(2) x is a multiple of 3.

The best/excellent answers get kudos.

(1) All odd integers are of the form 2k+1, and so upon division by 2, leave a remainder of 1. Sufficient.

(2) Multiples of 3 are of form 3m. If m is odd, 3m will leave a remainder of 1 with 2, if m is even 3m will leave a remainder of 0 with 2. Insufficient.

Hence, option A.
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