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Intern  Joined: 09 Apr 2010
Posts: 9
If x and y are positive integers, which of the following CAN  [#permalink]

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5
31 00:00

Difficulty:   65% (hard)

Question Stats: 54% (01:43) correct 46% (01:45) wrong based on 293 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
Math Expert V
Joined: 02 Sep 2009
Posts: 61544

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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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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: 9

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The correct answer is C though it beats me why. Any explanations will be very helpful.
Intern  Joined: 09 Apr 2010
Posts: 9

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But 35x/20y is an integer where x=4 and y=1
Intern  Joined: 09 Apr 2010
Posts: 9

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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 !
Manager  Joined: 14 Apr 2010
Posts: 128

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Hey...
why am i not able to comprehend this question? somebody please explain.... Intern  Affiliations: NYSSA
Joined: 07 Jun 2010
Posts: 28
Location: New York City
Schools: Wharton, Stanford, MIT, NYU, Columbia, LBS, Berkeley (MFE program)
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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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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.

GMAT assassins aren't born, they're made,
Rich
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Senior Manager  Joined: 07 Aug 2011
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If x and y are positive integers, which of the following CAN  [#permalink]

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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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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

Manager  Joined: 20 Dec 2013
Posts: 115
Re: If x and y are positive integers, which of the following CAN  [#permalink]

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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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Intern  Joined: 18 Nov 2015
Posts: 6
Re: If x and y are positive integers, which of the following CAN  [#permalink]

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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.

Non-Human User Joined: 09 Sep 2013
Posts: 14154
Re: If x and y are positive integers, which of the following CAN  [#permalink]

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_________________ Re: If x and y are positive integers, which of the following CAN   [#permalink] 03 Dec 2019, 19:24
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