Data Sufficiency

[manhattanmani]

If a is a positive integer and 81 divided by a results in remainder of 1, what is the value of a?
(1) the remainder when a is divided by 40 is 0
(2) the remainder when 40 is divided by a is 40

I dont understand how come statement 2 is sufficient?(as given in Advanced GMAT quant)

How could 40, when divided by a larger number than 40 gives remainder 40.
i tried with all , picking numbers etc.
can anyone please explain...

[jnelson0612]

If a is a positive integer and 81 divided by a results in remainder of 1, what is the value of a?
(1) the remainder when a is divided by 40 is 0
(2) the remainder when 40 is divided by a is 40

I dont understand how come statement 2 is sufficient?(as given in Advanced GMAT quant)

How could 40, when divided by a larger number than 40 gives remainder 40.
i tried with all , picking numbers etc.
can anyone please explain...

Sure! Let's look at the list of numbers that divide into 81 and gives a remainder of 1. We are likely talking about the factors of 80. They are 1, 80, 2, 40, 4, 20, 5, 16, 8, 10. Every one of these numbers will divide into 81 and leave a remainder of 1 except for 1, which divides evenly into 81. Thus, our possibilities for a are 2, 4, 5, 8, 10, 16, 20, 40, 80.

Statement 2 states that the remainder when 40 is divided by a is 40. Let's consider our options. 2, 4, 5, 8, 10, 20, and 40 all divide evenly into 40 and leave no remainder, so those cannot be a. That leaves 16 and 80. 16 divides into 40 leaving 2 remainder 8, so 16 is not a. a must be 80. 80 divides into 40 leaving 0 remainder 40. Sufficient. a is 80.

Please let us know if we can help further; thanks!

[manhattanmani]

If a is a positive integer and 81 divided by a results in remainder of 1, what is the value of a?
(1) the remainder when a is divided by 40 is 0
(2) the remainder when 40 is divided by a is 40

I dont understand how come statement 2 is sufficient?(as given in Advanced GMAT quant)

How could 40, when divided by a larger number than 40 gives remainder 40.
i tried with all , picking numbers etc.
can anyone please explain...

Sure! Let's look at the list of numbers that divide into 81 and gives a remainder of 1. We are likely talking about the factors of 80. They are 1, 80, 2, 40, 4, 20, 5, 16, 8, 10. Every one of these numbers will divide into 81 and leave a remainder of 1 except for 1, which divides evenly into 81. Thus, our possibilities for a are 2, 4, 5, 8, 10, 16, 20, 40, 80.

Statement 2 states that the remainder when 40 is divided by a is 40. Let's consider our options. 2, 4, 5, 8, 10, 20, and 40 all divide evenly into 40 and leave no remainder, so those cannot be a. That leaves 16 and 80. 16 divides into 40 leaving 2 remainder 8, so 16 is not a. a must be 80. 80 divides into 40 leaving 0 remainder 40. Sufficient. a is 80.

Please let us know if we can help further; thanks!

it seems i am losing on some basic concept but do you mean when 2 is divided by 4 = we get a remainder 2?
this 40/80 seems the same!?

[tim]

i'm not sure what you're asking with your final sentence, but 2 divided by 4 definitely gives a remainder of 2. go back to the definition of remainders if you're unsure..