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ruhi
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If x is a positive integer, is 'x' a multiple of 5? 1) 5 is 01 Dec 2004, 12:36
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If x is a positive integer, is 'x' a multiple of 5?
1) 5 is a factor of x/2.
2) 3x+5 is a multiple of 5



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If x is a positive integer, is 'x' a multiple of 5? 1) 5 is 01 Dec 2004, 16:51
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Pls explain why D ?


If x is a positive integer, is 'x' a multiple of 5?
1) 5 is a factor of x/2.
2) 3x+5 is a multiple of 5


Statement 1 - let take examples

x = 10 ......true
x=15 .......x/2 = 7.5 true as 1.5 * 5

x=3 ........x/2 =1.5 where 5 is a factor as 1.5 = 5 * 0.3 FALSE
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If x is a positive integer, is 'x' a multiple of 5? 1) 5 is 01 Dec 2004, 18:26
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statement 1 . yes and no
statement 2. 3x+5 is a multiple of 5, so 3x is a multiple of 5 => x is a multiple of 5.

ans B.
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If x is a positive integer, is 'x' a multiple of 5? 1) 5 is 01 Dec 2004, 21:02
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I will go for D.

I dont think you can have factors for fractions...
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If x is a positive integer, is 'x' a multiple of 5? 1) 5 is 02 Dec 2004, 00:26
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gmat+obsessed
Pls explain why D ?


If x is a positive integer, is 'x' a multiple of 5?
1) 5 is a factor of x/2.
2) 3x+5 is a multiple of 5


Statement 1 - let take examples

x = 10 ......true
x=15 .......x/2 = 7.5 true as 1.5 * 5

x=3 ........x/2 =1.5 where 5 is a factor as 1.5 = 5 * 0.3 FALSE
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gmat+obsessed, PLZ remember that 'x' is a POSITIVE INTEGER. hence , your example is invalid. The final answer of x should be a positive intege only.

The OA is D.
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If x is a positive integer, is 'x' a multiple of 5? 1) 5 is 02 Dec 2004, 01:08
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Ruhi,
Please elaborate your explanation......

The final answer of x should be a positive intege only. ==== Which number are u referring as final answer ?
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If x is a positive integer, is 'x' a multiple of 5? 1) 5 is 02 Dec 2004, 01:37
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Let x/2=5, x=10, which is a multiple of 5.
x/2=15, then x=30, which is also a multiple of 5.

you took x=7.5, 1.5 etc.. right? Well we cant take these values because it is given that x is a positive integer. 7.5, 1.5 etc.. are fractions and not integers... :)
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If x is a positive integer, is 'x' a multiple of 5? 1) 5 is 02 Dec 2004, 06:36
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gmat+obsessed
Pls explain why D ?
x=15 .......x/2 = 7.5 true as 1.5 * 5
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Remember you find factors of a number by determining their prime factors. You cannot do that with a fraction (7.5), so you cannot say 5 is a factor of 7.5.
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If x is a positive integer, is 'x' a multiple of 5? 1) 5 is 02 Dec 2004, 08:53
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If x is a positive integer, is 'x' a multiple of 5?
1) 5 is a factor of x/2.
2) 3x+5 is a multiple of 5

1) lets say x=8 .. 8/2=4 which is not a multiple of 5 for statement 1 to be valid the resultset of x/2 should be multiple of 5. that can only happen if x is a number which is divisible by 5. hence 1 is sufficient. x is multiple of 5.

2) 3x+5 is multiple of 5...

3(3)+5=14
3(5)+5=20
3(7)+5=21

looking above you can safely say that the expression 3x+5 would only be a multiple of 5 when x is multiple of 5.

hope it clear. :)
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If x is a positive integer, is 'x' a multiple of 5? 1) 5 is 02 Dec 2004, 15:43
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Ruhi,

does not sound convincing though....

you took x=7.5, 1.5 etc.. right? Well we cant take these values because it is given that x is a positive integer. 7.5, 1.5 etc.. are fractions and not integers... =========> My example took x=3 as example and which is integer...

the explanation given by gayathri sounds better that you take factors as prime numbers and cannot take fractions as factors.

Thanks all of you for ur explanations..its good to have such discussions....
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If x is a positive integer, is 'x' a multiple of 5? 1) 5 is 02 Dec 2004, 23:44
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gmat+obsessed
Ruhi,

does not sound convincing though....

you took x=7.5, 1.5 etc.. right? Well we cant take these values because it is given that x is a positive integer. 7.5, 1.5 etc.. are fractions and not integers... =========> My example took x=3 as example and which is integer...

the explanation given by gayathri sounds better that you take factors as prime numbers and cannot take fractions as factors.

Thanks all of you for ur explanations..its good to have such discussions....
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Hi,
what i meant to say is, since x is a positive integer, it has to remain so throughout, even when u consider the final answer, its still 'x', isnt it?? So how can you consider a fraction and decide whether a statement is sufficient or not.. i think its a very wrong approach.
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If x is a positive integer, is 'x' a multiple of 5? 1) 5 is 03 Dec 2004, 08:29
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I'd like to apply a different approach to the first one. We have all these phrases in the gmat to contend with:

x is a factor of y
x is a multiple of y
x is divisible by y
x is a divisor of y

They all say the same thing - they say that when you divide x and y, you get a whole number. Absolutely. You just have to figure out which one you're dividing.

For that, try an example. I always use 24 and 6.

6 is a factor of 24 --> 24/6 is integer
24 is a multiple of 6 --> 24/6 is integer
24 is divisible by 6 --> 24/6 is integer
6 is a divisor of 24 -- 24/6 is integer

So you can do the same thing with x and y, following the examples above, and figure out what's happening.

In this one, the question asks if x is a multiple of 5, so the question is really stating: is x/5 an integer?

1 states that 5 is a factor of x/2. Following the model above, that means that (x/2)/5 is an integer. And doing the math we find out that x/10 is an integer. If x divided by 10 is an integer, then x can be divided by all the factors of 10, including 5, so it's definately true.

For number 2, I agree with what's been written.

D

Hope that helps...



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