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# If m, n and p are digits and their product is a digit, what is value

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Math Expert
Joined: 02 Sep 2009
Posts: 52161
If m, n and p are digits and their product is a digit, what is value  [#permalink]

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19 Jan 2017, 07:05
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Difficulty:

85% (hard)

Question Stats:

37% (01:39) correct 63% (01:40) wrong based on 164 sessions

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If m, n and p are digits and their product is a digit, what is value of the product mnp?

(1) mn = 8
(2) m = 2n and n = 2p

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Re: If m, n and p are digits and their product is a digit, what is value  [#permalink]

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19 Jan 2017, 08:40
1
mnp = ?

St1: mn = 8 --> p can be 1 or 0.
mnp = 8 or mnp = 0
Not Sufficient.

St2: m = 2n and n = 2p --> mnp = 8(p^3) = 1 or 0.
Not Sufficient.

Combining St1 and St2, mn = 8 --> m or n cannot be 0 --> Hence p cannot be 0 --> mnp = 8.
Sufficient.

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Joined: 08 Jan 2017
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If m, n and p are digits and their product is a digit, what is value  [#permalink]

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19 Jan 2017, 13:12
Hi,

mnp=?

st1: as it doesn't give us the value for P it is not sufficient. for ex for p=0 mnp=0, and for p=1, mnp=8.

st2: it doesn't reveal any real value for any of variables so it is not sufficient.

st1+st2: m=2n=2(2p)=4p & mn=8=4p*2p=8p^2 therefore we have p=+1 or -1 . for p=-1, mnp=-8 & for p=1 mnp=8 which is not sufficient.
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Re: If m, n and p are digits and their product is a digit, what is value  [#permalink]

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20 Jan 2017, 20:59
Answer will be E because for "P" we have two values 1 & -1 by combining two given equations
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Re: If m, n and p are digits and their product is a digit, what is value  [#permalink]

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21 Jan 2017, 01:30
Since it is given that m,n and p are digits, they can assume either positive or negative value. Therefore E is the best answer
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Re: If m, n and p are digits and their product is a digit, what is value  [#permalink]

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23 Jan 2017, 12:49
clearly statement 1 is insufficient. Statement 2 is also insufficient because it only gives information about 2 of the 3 variables.

Combining both statements: 2n*n=8-->n=+/-4, m=+/-9, p=+/-2. Since there is no indications of whether the numbers are positive or negative, we don't have enough information to answer the question.

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Re: If m, n and p are digits and their product is a digit, what is value  [#permalink]

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23 Jan 2017, 19:47
Bunuel wrote:
If m, n and p are digits and their product is a digit, what is value of the product mnp?

(1) mn = 8
(2) m = 2n and n = 2p

answer will be C..
Digit(0-9)...
1.MN=8--------1 , we can have p =0 or 1,mnp=8 or mnp= 0
2.m=2n, n=2p
m=4p-----2
combining 1 and 2
m and n are not 0 from statement 1,so p cant be 0(from statement 2)..
MNP=8.
sufficient
so c
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Joined: 17 Sep 2016
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Re: If m, n and p are digits and their product is a digit, what is value  [#permalink]

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23 Jan 2017, 21:16
Good to read various explanations... I also thought answer to be C but correct one is E... Forgot to take n square as + or - 2 which makes two different answers when combined statements

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Joined: 02 Aug 2009
Posts: 7199
Re: If m, n and p are digits and their product is a digit, what is value  [#permalink]

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23 Jan 2017, 21:29
1
Bunuel wrote:
If m, n and p are digits and their product is a digit, what is value of the product mnp?

(1) mn = 8
(2) m = 2n and n = 2p

Hi
All those who have answered E will not be correct.
Reason.. there are only 10 digits : 0 to 9
-1 is a number made from digit 1..

1) mn is 8..
If P is 0, mnp is 0..
If p is 1, mnp is 8..
Insufficient

2) m=2n and n = 2p..
mnp= 4p*2p*p=8p^3..
p could be 0or 1..

Combined..
If p is 0, n =2p=2*0=0..
If this is so mn will be 0 and not 8..

So p is not 0 but 1 and mnp is 8*1=8
Sufficient
C
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3) effects of arithmetic operations : https://gmatclub.com/forum/effects-of-arithmetic-operations-on-fractions-269413.html

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Joined: 17 Sep 2016
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Re: If m, n and p are digits and their product is a digit, what is value  [#permalink]

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25 Jan 2017, 06:10
akhiparth wrote:
Good to read various explanations... I also thought answer to be C but correct one is E... Forgot to take n square as + or - 2 which makes two different answers when combined statements

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Answer will be C... Difference between digit & integer applies here

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Re: If m, n and p are digits and their product is a digit, what is value  [#permalink]

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06 Feb 2018, 10:36
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# If m, n and p are digits and their product is a digit, what is value

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