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# If k, (k+200), (k+350), and 15*K are all multiples of P, the

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If k, (k+200), (k+350), and 15*K are all multiples of P, the  [#permalink]

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20 Jun 2014, 00:39
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67% (01:53) correct 33% (02:05) wrong based on 269 sessions

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If k, (k+200), (k+350), and 15*K are all multiples of P, then P could equal which of the following ?

A. 20
B. 25
C. 75
D. 100
E. 150
Math Expert
Joined: 02 Sep 2009
Posts: 55635
Re: If k, (k+200), (k+350), and 15*K are all multiples of P, the  [#permalink]

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20 Jun 2014, 00:56
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guerrero25 wrote:
If k, (k+200), (k+350), and 15*K are all multiples of P, then P could equal which of the following ?

A. 20
B. 25
C. 75
D. 100
E. 150

{Multiple of p} - {Multiple of p} = {Multiple of p}.

(K+200) - k = 200 = {Multiple of p}.
(K+350) - k = 350 = {Multiple of p}.

Both 200 and 350 are multiples of only option B.

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Re: If k, (k+200), (k+350), and 15*K are all multiples of P, the  [#permalink]

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11 Jan 2015, 22:09
trail and error since question is asking about may be value any value satisfying the conditions is the answer 25 is the answer hence
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Re: If K, (K+200), (K+350), and 15*K are all multiples of P  [#permalink]

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27 Jun 2017, 19:29
mkrishnabdrr wrote:
If K, (K+200), (K+350), and 15*K are all multiples of P, then P could equal which of the following?
A. 20
B. 25
C. 75
D. 100
E. 150

substiute each value in options given to value K and check if it is divisible by P

(1) K=20 then K+350 = 370 not div by 20...NO
(2) K=25 ...All values K, (K+200), (K+350), and 15*K are div by 25--YES
(3) k= 75 then K+200= 275 not div by 75...NO
(4) k=100 then K+350 = 450 not div by 100...NO
(5) 150 then K+200 =350 not div by 150...NO

Ans B
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If K, (K+200), (K+350), and 15*K are all multiples of P  [#permalink]

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27 Jun 2017, 19:54
Imo B
I did by substituting values of option .
Is there any other method by which we can solve this question?
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Re: If K, (K+200), (K+350), and 15*K are all multiples of P  [#permalink]

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27 Jun 2017, 20:32
mkrishnabdrr wrote:
If K, (K+200), (K+350), and 15*K are all multiples of P, then P could equal which of the following?
A. 20
B. 25
C. 75
D. 100
E. 150

Hi
A logical method apart from substitution is
If two numbers are divisible by P, their difference will also be div by P
So k +200 - k=200 is div by P
K+350-k=350 is div by P.
You can stop here or move onto next.
So both 200 and 350 are div by P, and HCF of 200&350 is 50..
In choices only 25 is factor of 50
B

If 150 is the answer, it's Factors 25 and 75 can also be the answer but we cannot have THREE answers, so higher multiple are out .. ONLY 25 is possible in these three.
Similarly in 20 and 100 ONLY 20 is possible.
Now you can find through substitution for only 20 and 25, eliminate all other choices
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Re: If k, (k+200), (k+350), and 15*K are all multiples of P, the  [#permalink]

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27 Jun 2017, 21:10
chetan2u wrote:
mkrishnabdrr wrote:
If K, (K+200), (K+350), and 15*K are all multiples of P, then P could equal which of the following?
A. 20
B. 25
C. 75
D. 100
E. 150

Hi
A logical method apart from substitution is
If two numbers are divisible by P, their difference will also be div by P
So k +200 - k=200 is div by P
K+350-k=350 is div by P.
You can stop here or move onto next.
So both 200 and 350 are div by P, and HCF of 200&350 is 50..
In choices only 25 is factor of 50
B

If 150 is the answer, it's Factors 25 and 75 can also be the answer but we cannot have THREE answers, so higher multiple are out .. ONLY 25 is possible in these three.
Similarly in 20 and 100 ONLY 20 is possible.
Now you can find through substitution for only 20 and 25, eliminate all other choices

Hi thanks chetan2u
i always get stuck in question involving like these , can you give me some tips regarding number properties.
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Re: If k, (k+200), (k+350), and 15*K are all multiples of P, the  [#permalink]

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28 Jun 2017, 07:51
guerrero25 wrote:
If k, (k+200), (k+350), and 15*K are all multiples of P, then P could equal which of the following ?

A. 20
B. 25
C. 75
D. 100
E. 150

This question needs to be solved very carefully.

So we have to check values form option which can completely divide k, k+200, k+350, 15k
SO the number which will divide k will also divide 15k . so no need to check 15k
For the k+200 & k+350 , number must divide 200 & 350 respectively

So lets check with 20, 200 - Yes, 350 - No
25, 200 yes , 350 yes
75 , 200 No , 350 No
100, 200 Yes, 350 No
150, 200 No, 350 No

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Re: If k, (k+200), (k+350), and 15*K are all multiples of P, the  [#permalink]

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10 Sep 2018, 01:20
chetan2u wrote:
mkrishnabdrr wrote:
If K, (K+200), (K+350), and 15*K are all multiples of P, then P could equal which of the following?
A. 20
B. 25
C. 75
D. 100
E. 150

Hi
A logical method apart from substitution is
If two numbers are divisible by P, their difference will also be div by P
So k +200 - k=200 is div by P
K+350-k=350 is div by P.
You can stop here or move onto next.
So both 200 and 350 are div by P, and HCF of 200&350 is 50..
In choices only 25 is factor of 50
B

If 150 is the answer, it's Factors 25 and 75 can also be the answer but we cannot have THREE answers, so higher multiple are out .. ONLY 25 is possible in these three.
Similarly in 20 and 100 ONLY 20 is possible.
Now you can find through substitution for only 20 and 25, eliminate all other choices

Would it be correct to say the following:

since k+350 is divisible by P, that implies: k is divisible by P and 350 is divisible by P?

thanks
Re: If k, (k+200), (k+350), and 15*K are all multiples of P, the   [#permalink] 10 Sep 2018, 01:20
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