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# If x and y are positive integers, which of the following CAN

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Intern
Joined: 09 Apr 2010
Posts: 12
If x and y are positive integers, which of the following CAN  [#permalink]

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01 Jun 2010, 13:18
5
28
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Difficulty:

65% (hard)

Question Stats:

58% (01:44) correct 42% (01:51) wrong based on 361 sessions

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If x and y are positive integers, which of the following CANNOT be the greatest common divisor of 35x and 20y?

(A) 5
(B) 5(x – y)
(C) 20x
(D) 20y
(E) 35x
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Joined: 02 Sep 2009
Posts: 52161

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07 Jun 2010, 09:04
1
6
bibha wrote:
Hey...
why am i not able to comprehend this question? somebody please explain....

If x and y are positive integers, which of the following CANNOT be the greatest common divisor of 35x and 20y?

A. 5
B. 5(x – y)
C. 20x
D. 20y
E. 35x

Greatest common divisor (GCD) of $$35x$$ and $$20y$$ obviously must be a divisor of both $$35x$$ and $$20y$$, which means $$\frac{35x}{GCD}$$ and $$\frac{20y}{GCD}$$ must be an integer.

If $$GCD=20x$$ (option C), then $$\frac{35x}{20x}=\frac{7}{4}\neq{integer}$$, which means that $$20x$$ cannot be GCD of $$35x$$ and $$20y$$ as it is not a divisor of $$35x$$.

How about the other choices, can they be GCD of $$35x$$ and $$20y$$?

A. $$5$$ --> if $$x=y=1$$ --> $$35x=35$$ and $$20y=20$$ --> $$GCD(35,20)=5$$. Answer is YES, $$5$$ can be GCD of $$35x=35$$ and $$20y$$;

B. $$5(x-y)$$ --> if $$x=3$$ and $$y=2$$ --> $$35x=105$$ and $$20y=40$$ --> $$GCD(105,40)=5=5(x-y)$$. Answer is YES, $$5(x-y)$$ can be GCD of $$35x$$ and $$20y$$;

D. $$20y$$ --> if $$x=4$$ and $$y=1$$ --> $$35x=140$$ and $$20y=20$$ --> $$GCD(140,20)=20=20y$$. Answer is YES, $$20y$$ can be GCD of $$35x$$ and $$20y$$;

E. $$35x$$ --> if $$x=1$$ and $$y=7$$ --> $$35x=35$$ and $$20y=140$$ --> $$GCD(35,140)=35=35x$$. Answer is YES, $$35x$$ can be GCD of $$35x$$ and $$20y$$.

Hope it's clear.
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01 Jun 2010, 13:41
2
4
priyanka116 wrote:
If x and y are positive integers, which of the following CANNOT be the greatest common divisor of 35x and 20y?

A) 5
B) 5(x – y)
C) 20x
D) 20y
E) 35x

The reason the answer is C is because if you divide 35x/20x, you get 35/20, which isn't an integer. 35x and 20y can be divisible by 5, and 5(x-y) eg x=5, y=4. 35x/20y, if y = 7, and X=4, 20y/20y = 1. E also works, 35x/35x = 1, 20y/35x works when Y=7, X=4
##### General Discussion
Intern
Joined: 09 Apr 2010
Posts: 12

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01 Jun 2010, 13:19
The correct answer is C though it beats me why. Any explanations will be very helpful.
Intern
Joined: 09 Apr 2010
Posts: 12

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01 Jun 2010, 13:53
But 35x/20y is an integer where x=4 and y=1
Intern
Joined: 09 Apr 2010
Posts: 12

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01 Jun 2010, 13:55
I must be shaken awake to see the obvious and obvious making a fool of myself! My bad... I get it.... its not 35x/20y its 35x/20x.. thanks !
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Joined: 14 Apr 2010
Posts: 179

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07 Jun 2010, 05:03
Hey...
why am i not able to comprehend this question? somebody please explain....
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18 Jun 2010, 11:30
edoy56 wrote:
priyanka116 wrote:
If x and y are positive integers, which of the following CANNOT be the greatest common divisor of 35x and 20y?

A) 5
B) 5(x – y)
C) 20x
D) 20y
E) 35x

The reason the answer is C is because if you divide 35x/20x, you get 35/20, which isn't an integer. 35x and 20y can be divisible by 5, and 5(x-y) eg x=5, y=4. 35x/20y, if y = 7, and X=4, 20y/20y = 1. E also works, 35x/35x = 1, 20y/35x works when Y=7, X=4

Hahaha. I'm so stupid... thats the 10 sec answer...
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Re: If x and y are positive integers, which of the following CAN  [#permalink]

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29 Dec 2014, 07:34
Hi All,

This question can be solved by TESTing VALUES. Here though, we'll be TESTing VALUES to prove which answers are POSSIBLE (so that we can eliminate them). This prompt is actually built around a few Number Properties and we can actually use the answer choices to our advantage (instead of just randomly TESTing VALUES until we knock out four of the answers).

We're told that X and Y are POSITIVE INTEGERS. We're asked which of the 5 answers CANNOT be the GCD of 35X and 20Y. This means that 4 of the answers COULD be the GCD under certain circumstances.

Before we TEST anything, there are some things to note about 35X and 20Y:

1) 20Y will ALWAYS be EVEN (20, 40, 60, 80, 100, etc.)
2) 35X can be EVEN or ODD (35, 70, 105, 140, etc.)

Looking at the list of answer choices, there are some that we can quickly eliminate...

IF
X = 1
Y = 1
Then we have 35 and 20, so the GCD = 5
Eliminate A.

X = 20
Y = 1
Then we have 700 and 20, so the GCD = 20
Eliminate D.

X = 1
Y = 35
Then we have 35 and 700, so the GCD = 35
Eliminate E.

With the remaining 2 answers, we have to think a little more.

To get a simple example of 5(X-Y) to be the GCD, we probably need 35X to be ODD

IF...
X = 3
Y = 2
Then we have 105 and 40, so the GCD = 5
5(X-Y) = 5(3-2) = 5
This can ALSO be the GCD
Eliminate B.

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If x and y are positive integers, which of the following CAN  [#permalink]

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09 Jan 2015, 20:06
priyanka116 wrote:
If x and y are positive integers, which of the following CANNOT be the greatest common divisor of 35x and 20y?

(A) 5
(B) 5(x – y)
(C) 20x
(D) 20y
(E) 35x

option
A) x=y=1; 5 is GCD.
2) x=3;y=2; 5(x-y) is GCD
3) 35x/20x cannot be an integer. ->Correct answer.
4) at X=20Y; 20y will be gcd.
5) at y=35x; 35x will be gcd.
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Re: If x and y are positive integers, which of the following CAN  [#permalink]

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13 Jan 2015, 21:34
In this type of question, we need to substitute value of "x" & "y" with positive integer as 2 & 1 etc.

Otherwise, we can end up in a wrong answer. Algebraic solution from the options is not possible

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Re: If x and y are positive integers, which of the following CAN  [#permalink]

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13 Jan 2015, 21:40
priyanka116 wrote:
If x and y are positive integers, which of the following CANNOT be the greatest common divisor of 35x and 20y?

(A) 5
(B) 5(x – y)
(C) 20x
(D) 20y
(E) 35x

Number divided by HCF should be an integer.

35x divided by 20x is not an integer hence 20x cannot be the HCF.
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Re: If x and y are positive integers, which of the following CAN  [#permalink]

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15 May 2016, 08:36
Property : GCD of any 2 numbers must divide those numbers completely.
Looking at the options : 20x can never divide 35x completely, all other options can be true.

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Re: If x and y are positive integers, which of the following CAN  [#permalink]

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05 Feb 2018, 06:51
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