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# If x and y are positive integers such that y is a multiple of 5 and 3x

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If x and y are positive integers such that y is a multiple of 5 and 3x [#permalink]

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14 Jun 2016, 15:38
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If x and y are positive integers such that y is a multiple of 5 and 3x + 4y = 200, then x must be a multiple of which of the following?

A) 3

B) 6

C) 7

D) 8

E) 10

OG 2017 New Question
[Reveal] Spoiler: OA

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Re: If x and y are positive integers such that y is a multiple of 5 and 3x [#permalink]

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14 Jun 2016, 15:57
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AbdurRakib wrote:
If x and y are positive integers such that y is a multiple of 5 and 3x + 4y = 200, then x must be a multiple of which of the following?

A) 3

B) 6

C) 7

D) 8

E) 10

OG 2017 New Question

If y is a multiple of 5, then we know that y = 5k for some integer k.
So, let's take 3x + 4y = 200 and replace y with 5k to get: 3x + 4(5k) = 200
Simplify to get: 3x + 20k = 200 (where k is some integer)
Subtract 20k from both sides to get: 3x = 200 - 20k
Divide both sides by 3 to get: x = (200 - 20k)/3
Now factor the numerator to get: x = (20)(10 - k)/3
Since x must be an integer, and since 20/3 is not an integer, it must be the case that (10 - k)/3 evaluates to be some integer.
In other words, x = (20)(some integer)
So, x must be a multiple of 20. However, 20 is not one of the answer choices.
Then again, we can rewrite x to get: x = (2)(10)(some integer)
This tells us that x must also be a multiple of 10

[Reveal] Spoiler:
E

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Re: If x and y are positive integers such that y is a multiple of 5 and 3x [#permalink]

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14 Jun 2016, 22:12
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AbdurRakib wrote:
If x and y are positive integers such that y is a multiple of 5 and 3x + 4y = 200, then x must be a multiple of which of the following?

A) 3

B) 6

C) 7

D) 8

E) 10

OG 2017 New Question

If y is a multiple of 5, 4y must be a multiple of 5 too.

3x = 200 - 4y = Multiple of 5 - Multiple of 5 = Multiple of 5

Since 3 is not a multiple of 5, x MUST be a multiple of 5.

Also, 4y is even. So 3x = Even - Even = Even
Since 3 is not even, x must be even.

Hence x must be a multiple of 10.

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Get started with Veritas Prep GMAT On Demand for $199 Veritas Prep Reviews Kudos [?]: 17843 [16], given: 235 Manager Joined: 04 Apr 2015 Posts: 133 Kudos [?]: -24 [1], given: 47 Re: If x and y are positive integers such that y is a multiple of 5 and 3x [#permalink] ### Show Tags 14 Jun 2016, 22:25 1 This post received KUDOS its given y is multiple of 5 therefore 4y is even and will end in zero as even multiple of 5 ends in zero(zero at units place) now equation 3x + 4y =200, as we know 4y ends in zero (zero at units place ) we need to add something that ends in zero (zero at units place) to get to 200,3x can only end in zero if x is multiple of 10 Kudos [?]: -24 [1], given: 47 Intern Joined: 23 Nov 2016 Posts: 1 Kudos [?]: 6 [6], given: 15 GRE 1: 325 Q164 V161 Re: If x and y are positive integers such that y is a multiple of 5 and 3x [#permalink] ### Show Tags 28 Nov 2016, 10:32 6 This post received KUDOS If x and y are positive integers such that y is a multiple of 5 and 3x + 4y = 200, then x must be a multiple of which of the following? A) 3 B) 6 C) 7 D) 8 E) 10 ---------------------- I drowned in these numbers and failed on my first attempt at this question, but I've got it now. The most simple approach I can think of is to plug in values of y that are multiples of 5. 1) Plug in 5, 10, 15, & 20. 2) These yield equations of: 3x = 180 3x= 160 3x = 140 3x = 120 3) Of our answer choices, (E) 10 is the only # that divides evenly in all these situations, therefore it must be our answer. Kudos [?]: 6 [6], given: 15 Veritas Prep GMAT Instructor Joined: 16 Oct 2010 Posts: 7745 Kudos [?]: 17843 [4], given: 235 Location: Pune, India Re: If x and y are positive integers such that y is a multiple of 5 and 3x [#permalink] ### Show Tags 28 Nov 2016, 19:45 4 This post received KUDOS Expert's post VeritasPrepKarishma wrote: AbdurRakib wrote: If x and y are positive integers such that y is a multiple of 5 and 3x + 4y = 200, then x must be a multiple of which of the following? A) 3 B) 6 C) 7 D) 8 E) 10 OG 2017 New Question If y is a multiple of 5, 4y must be a multiple of 5 too. 3x = 200 - 4y = Multiple of 5 - Multiple of 5 = Multiple of 5 Since 3 is not a multiple of 5, x MUST be a multiple of 5. Also, 4y is even. So 3x = Even - Even = Even Since 3 is not even, x must be even. Hence x must be a multiple of 10. Answer (E) Responding to a pm: Quote: If 3x has to be even, why can't the answer be B oder D, since 3*6 = even and 3*8 = even? You are given that y is a multiple of 5. So 4y is a multiple of 10. Hence 3x = 200 - 4y = Multiple of 10 - Multiple of 10 So 3x would be a multiple of 10 too. So the answer cannot be (B) or (D) _________________ Karishma Veritas Prep | GMAT Instructor My Blog Get started with Veritas Prep GMAT On Demand for$199

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Re: If x and y are positive integers such that y is a multiple of 5 and 3x [#permalink]

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02 Dec 2016, 10:45
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AbdurRakib wrote:
If x and y are positive integers such that y is a multiple of 5 and 3x + 4y = 200, then x must be a multiple of which of the following?

A) 3

B) 6

C) 7

D) 8

E) 10

We are given that x and y are positive integers such that y is a multiple of 5 and 3x + 4y = 200. We need to determine which answer choice MUST be a multiple of x.

Because y is a multiple of 5, we can represent y as 5k, in which k is an integer, and we have:

3x + 4(5k) = 200

3x + 20k = 200

Since the sum of 3x and 20k is 200 (or a number that has a units digit of zero), and since 20k has a units digit of zero, 3x must also contain a units digit of zero. The only way for 3x to contain a units digit of zero is if it’s multiplied by a multiple of 10. Thus, x must be a multiple of 10.

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Re: If x and y are positive integers such that y is a multiple of 5 and 3x [#permalink]

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02 Dec 2016, 11:18
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AbdurRakib wrote:
If x and y are positive integers such that y is a multiple of 5 and 3x + 4y = 200, then x must be a multiple of which of the following?

A) 3

B) 6

C) 7

D) 8

E) 10

OG 2017 New Question

Plug in values and check -

Let y = 5 ; 3x + 4y = 200

So, 3x + 20 = 200

Or, x = 60 ( Options C & D rejected , Left with options A, B & E )

Let y = 20 ; 3x + 4y = 200

So, 3x + 80 = 200

Or, x = 40 ( Options A &B rejected , Left with option E )

Hence, answer will be optin (E)

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Re: If x and y are positive integers such that y is a multiple of 5 and 3x [#permalink]

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25 Mar 2017, 06:08
We know: 1. x and y are positive integers
2. y is a multiple of 5
3. 3x + 4y = 200

3x + 4y = 200

=> 3x = 200 - 4y

It's known that if we add or subtract multiples of N, the result is a multiple of N. Here, both 200 and 4y are multiple of 10(20 actually). So 3x is a multiple of 10.
And therefore x is a multiple of 10.

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Re: If x and y are positive integers such that y is a multiple of 5 and 3x [#permalink]

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25 Mar 2017, 09:40
AbdurRakib wrote:
If x and y are positive integers such that y is a multiple of 5 and 3x + 4y = 200, then x must be a multiple of which of the following?

A) 3

B) 6

C) 7

D) 8

E) 10

let y=35
x=20
only E works

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Re: If x and y are positive integers such that y is a multiple of 5 and 3x [#permalink]

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28 Apr 2017, 10:49
I approached this in a different style I think than the other posters - is this way correct as well?

First, 200 factors down to $$2^3 * 5^2$$

Looking at the information we know that from the equation $$3x + 4y$$, where y is a multiple of 5, we have the factors of $$2^2$$ (from the 4), 3, and 5. Given this, we can then determine that we need one more factor of both 2 and 5. E - 10 is the only answer choice that provides those two factors.

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Re: If x and y are positive integers such that y is a multiple of 5 and 3x [#permalink]

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01 May 2017, 10:54
GMATPrepNow wrote:
AbdurRakib wrote:
If x and y are positive integers such that y is a multiple of 5 and 3x + 4y = 200, then x must be a multiple of which of the following?

A) 3

B) 6

C) 7

D) 8

E) 10

OG 2017 New Question

If y is a multiple of 5, then we know that y = 5k for some integer k.
So, let's take 3x + 4y = 200 and replace y with 5k to get: 3x + 4(5k) = 200
Simplify to get: 3x + 20k = 200 (where k is some integer)
Subtract 20k from both sides to get: 3x = 200 - 20k
Divide both sides by 3 to get: x = (200 - 20k)/3
Now factor the numerator to get: x = (20)(10 - k)/3
Since x must be an integer, and since 20/3 is not an integer, it must be the case that (10 - k)/3 evaluates to be some integer.
In other words, x = (20)(some integer)
So, x must be a multiple of 20. However, 20 is not one of the answer choices.
Then again, we can rewrite x to get: x = (2)(10)(some integer)
This tells us that x must also be a multiple of 10

[Reveal] Spoiler:
E

Here we say that (10-k)/3 = (some-int) => (10-k) = 3*(some-int)
and x = 20*(10-k)/3
x = 20*3*(some-int)
so x is a multiple of 3 as well.

Where am I going wrong?

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Re: If x and y are positive integers such that y is a multiple of 5 and 3x [#permalink]

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30 Jun 2017, 02:46
this is hard

3x+4y=200
y=(200-3x)/4

= 50-3x/4

because y is divisible by 5, 3x/5 is divisible by 5

3x/4=5a
x=20a/3

a must divisible by 3, so that x can be interger, so x= multiple of 20

x divisible by 10

hard one

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If x and y are positive integers such that y is a multiple of 5 and 3x [#permalink]

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07 Sep 2017, 23:50
x and y are positive integers

This is the most important information that will help us find the answer.

y=5k (k is a positive constant)

3x+4*5k= 200
3x+20k= 200
x= (200-20k)/3

x= 20(10-k)/3

As x is an integer, the above equation has to be an integer. As 20 is not divisible by 3, (10-k) must be divisible by 3 to make RHS an integer.

Looking at the options, E works.
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If x and y are positive integers such that y is a multiple of 5 and 3x [#permalink]

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09 Sep 2017, 10:01
AbdurRakib wrote:
If x and y are positive integers such that y is a multiple of 5 and 3x + 4y = 200, then x must be a multiple of which of the following?

A) 3

B) 6

C) 7

D) 8

E) 10

OG 2017 New Question

3x+4y=200➡3x=4(50-y)
because y is a multiple of 5, and 4 is even,
4(50-y) will always have a units digit of 0
10
E

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Re: If x and y are positive integers such that y is a multiple of 5 and 3x [#permalink]

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14 Sep 2017, 23:07
3x + 4y = 200
y is a multiple of 5 so go for the trail and error
1. 3x+4*5 = 200
3x = 180, it is mutiple of both 3 and 10
2. 3x+4*(5*2) = 200
3x = 160, 3 can be eliminated so answer should be 10
E
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Re: If x and y are positive integers such that y is a multiple of 5 and 3x [#permalink]

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22 Sep 2017, 09:45
VeritasPrepKarishma wrote:
AbdurRakib wrote:
If x and y are positive integers such that y is a multiple of 5 and 3x + 4y = 200, then x must be a multiple of which of the following?

A) 3

B) 6

C) 7

D) 8

E) 10

OG 2017 New Question

If y is a multiple of 5, 4y must be a multiple of 5 too.

3x = 200 - 4y = Multiple of 5 - Multiple of 5 = Multiple of 5

Since 3 is not a multiple of 5, x MUST be a multiple of 5.

Also, 4y is even. So 3x = Even - Even = Even
Since 3 is not even, x must be even.

Hence x must be a multiple of 10.

hi mam

The way I approached the problem is as under:

3x + 4y = 200
Now, as, y = 5k

3x + 20k = 200

x = 20(10 - k)/3
Now, (10 - k) must be 3n

So, x = 60n

Thus answer choice E must be true, and other choices could be true ....

please say to me whether it is okay...

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If x and y are positive integers such that y is a multiple of 5 and 3x [#permalink]

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22 Sep 2017, 10:23
AbdurRakib wrote:
If x and y are positive integers such that y is a multiple of 5 and 3x + 4y = 200, then x must be a multiple of which of the following?

A) 3

B) 6

C) 7

D) 8

E) 10

OG 2017 New Question

3x/4+y=50
x=either 20 or 40
10
E

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Re: If x and y are positive integers such that y is a multiple of 5 and 3x [#permalink]

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26 Sep 2017, 01:37
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gmatcracker2017 wrote:
VeritasPrepKarishma wrote:
AbdurRakib wrote:
If x and y are positive integers such that y is a multiple of 5 and 3x + 4y = 200, then x must be a multiple of which of the following?

A) 3

B) 6

C) 7

D) 8

E) 10

OG 2017 New Question

If y is a multiple of 5, 4y must be a multiple of 5 too.

3x = 200 - 4y = Multiple of 5 - Multiple of 5 = Multiple of 5

Since 3 is not a multiple of 5, x MUST be a multiple of 5.

Also, 4y is even. So 3x = Even - Even = Even
Since 3 is not even, x must be even.

Hence x must be a multiple of 10.

hi mam

The way I approached the problem is as under:

3x + 4y = 200
Now, as, y = 5k

3x + 20k = 200

x = 20(10 - k)/3
Now, (10 - k) must be 3n

So, x = 60n

Thus answer choice E must be true, and other choices could be true ....

please say to me whether it is okay...

Yes, perfectly fine.
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Re: If x and y are positive integers such that y is a multiple of 5 and 3x [#permalink]

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22 Oct 2017, 17:59
I think the trick here is to use unit digit concept.
3X+20K=200 means 3X must have 0 as unit digit.
from the answer choices, only E works.

Thanks
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Re: If x and y are positive integers such that y is a multiple of 5 and 3x   [#permalink] 22 Oct 2017, 17:59
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