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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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New post 19 Jun 2014, 23:39
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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
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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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New post 19 Jun 2014, 23:56
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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.

Answer: 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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New post 11 Jan 2015, 21:09
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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New post 27 Jun 2017, 18:29
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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New post 27 Jun 2017, 18:54
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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New post 27 Jun 2017, 19:32
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

Choices can also help you in a big way.
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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New post 27 Jun 2017, 20:10
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

Choices can also help you in a big way.
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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New post 28 Jun 2017, 06:51
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

Answer 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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New post 10 Sep 2018, 00:20
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

Choices can also help you in a big way.
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
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Re: If k, (k+200), (k+350), and 15*K are all multiples of P, the &nbs [#permalink] 10 Sep 2018, 00:20
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