cannot be x + y?

[sanju09]

If x and y are positive integers, and x is a multiple of 5 and y is a multiple of 8, then which of the following cannot be x + y?
A. 45
B. 42
C. 39
D. 36
E. 32



[spoiler]made up by Sanjeev K Saxena for Avenues Abroad[/spoiler]

[Anurag@Gurome]

If x is a multiple of 5 and y is a multiple of 8, then which of the following cannot be x + y?
A. 45
B. 42
C. 39
D. 36
E. 32
[spoiler]made up by Sanjeev K Saxena for Avenues Abroad[/spoiler]

A. 45 = 5 (multiple of 5) + 40 (multiple of 8); possible
B. 42 = 10 (multiple of 5) + 32 (multiple of 8); possible
C. 39 = 15 (multiple of 5) + 24 ( multiple of 8); possible
D. 36 = 20 (multiple of 5) + 16 (multiple of 8); possible
E. 32 = 0 (multiple of 5) + 32 (multiple of 8); possible

Note: 0 is a multiple of all numbers.

[ubhanja]

39 can be expressed as 8*3 + 5* 3=39

I am not sure of the source of this question. But 32 can be the answer, not sure if we can consider 0 as a mutiple

[LalaB]

IMO, both C and E are correct, and q. needs to be modified.

[pemdas]

IOM question needs to be re-developed.
The multiplies can be either positive or negative values, as the problem doesn't state explicitly sign(s) of x and y. None of the choices will fit, and 0 is the multiple of all numbers.

[karthikgmat]

E is the answer,, but is 0 not a multiple of 5?

[sanju09]

IMO, both C and E are correct, and q. needs to be modified.

A multiple of all numbers in the universe is ambiguous to refer in hidden, on real GMAT; hence neither x nor y can be taken as 0 here. I would like to see more expert comments on this issue, please. I would also like to know what stops us believe that x and y are positive integers here; we shouldn't forget that whenever GMAT uses the terms like divisible, a factor of, or a multiple of, they invariably mean non negative integers, preferably positive ones in most of the cases.

[pemdas]

too many assumptions embedded in this question ...

IMO, both C and E are correct, and q. needs to be modified.

A multiple of all numbers in the universe is ambiguous to refer in hidden, on real GMAT; hence neither x nor y can be taken as 0 here ?. I would like to see more expert comments on this issue, please. I would also like to know what stops us believe that x and y are positive integers here ?; we shouldn't forget that whenever GMAT uses the terms like divisible, a factor of, or a multiple of, they invariably mean non negative integers, preferably positive ones in most of the cases ?.

@sanju, official GMAT questions don't invariably mean, they do mention a positive integer term in each case. If you don't mention the sign of values, they are considered either positive or negative or non-negative.

Here is the list of questions from OG-12 which test the 'multiple' properties: diagnostic test question # 23, PS sample question # 201, DS sample questions # 82, 90

p.s. it's quite "witty" to make up an ambiguous question and then to try to defend its content. This question is badly developed and the only way a GMAT taker could benefit from it, if the question is re-developed.

[Mike@Magoosh]

A multiple of all numbers in the universe is ambiguous to refer in hidden, on real GMAT; hence neither x nor y can be taken as 0 here. I would like to see more expert comments on this issue, please. I would also like to know what stops us believe that x and y are positive integers here; we shouldn't forget that whenever GMAT uses the terms like divisible, a factor of, or a multiple of, they invariably mean non negative integers, preferably positive ones in most of the cases.

I'm happy to put in my 2-cents here.

When we just say "x is a multiple of 5", that means that x = 5*z, where z is some integer. Thus, all the multiples of 5 are {. . . -15, -10, -5, 0, 5, 10, 15, . . . } That's not the least bit ambiguous. That's precisely how mathematicians understand the word "multiple."

Given that, all five answer choices can be possible values of x+y, as demonstrated amply above. Zero is properly a multiple of each and every integer. Again, nothing is the least bit ambiguous about that.

Even if we explicitly specify that neither x nor y can equal zero, that doesn't eliminate the difficulty, because negative multiples still remain, and

32 = 72 + (-40) = 112 + (-80) = etc.
32 = (-8) + 40 = (-48) + 80 = etc.

In fact, an infinite number of pairs of the form (multiple of 8, multiple of 5) have a sum of 32. In fact, given any odd number and any even number, as along as the two numbers are relatively prime to one another, then an infinite number of pairs of their multiples will add to any particular sum -- a cool little fact.

I believe the snafu is simply in the problem's set-up. Real GMAT math questions often involve some technical specifications for precisely this reason. If we rephrase the prompt as:

If x and y are positive integers, and x is a multiple of 5 and y is a multiple of 8, then which of the following cannot be x + y?

. . . then the problem is well-defined with well-defined answer, E.

If the creator of a GMAT math problem has a particular restriction in mind, it's very important to state this restriction explicitly in the text of the problem. If you mean positive integers, you need to say positive integers. Such precision is necessary to meet the rigorous standards of the GMAT.

Does all this make sense? Please let me know if anyone reading this has any questions at all.

Mike

[sanju09]

Agreed and edited!