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Senior Manager  Joined: 06 Aug 2011
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If N is a two-digit even integer, is N < 20?  [#permalink]

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Question Stats: 40% (02:14) correct 60% (01:55) wrong based on 258 sessions

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If N is a two-digit even integer, is N < 20?

(1) The product of the digits of N is less than the sum of the digits of N.

(2) The product of the digits of N is positive.

_________________
Bole So Nehal.. Sat Siri Akal.. Waheguru ji help me to get 700+ score !
Math Expert V
Joined: 02 Sep 2009
Posts: 59722
Re: If N is a two-digit even integer, is N < 20?  [#permalink]

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5
Mountain14 wrote:
I am getting A as answer....

Not sure how C....is OA..

If N is a two-digit even integer, is N < 20?

(1) The product of the digits of N is less than the sum of the digits of N. This case is possible only if either digit is 0 or 1. For example, N can be 10, 12, 14, 16, 18, 20, 30, 40, ... So, N can be less as well as greater or equal to 20. Not sufficient.

(2) The product of the digits of N is positive. This implies that neither of the digits of N is zero. N still can be be less as well as greater than 20, for example, consider 12 or 22. Not sufficient.

(1)+(2) Since neither of the digits of N is zero, then values of N like 20, 30, 40, ... are not possible, thus N is definitely less than 20 (12, 14, 16, 18). Sufficient.

Hope it's clear.
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Senior Manager  Joined: 06 Aug 2011
Posts: 317
Re: If N is a two-digit even integer, is N < 20?  [#permalink]

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sanjoo wrote:
If N is a two-digit even integer, is N < 20?

(1) The product of the digits of N is less than the sum of the digits of N.

(2) The product of the digits of N is positive.

What if N is 21??

i chose E
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Bole So Nehal.. Sat Siri Akal.. Waheguru ji help me to get 700+ score !
Math Expert V
Joined: 02 Sep 2009
Posts: 59722
Re: If N is a two-digit even integer, is N < 20?  [#permalink]

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sanjoo wrote:
sanjoo wrote:
If N is a two-digit even integer, is N < 20?

(1) The product of the digits of N is less than the sum of the digits of N.

(2) The product of the digits of N is positive.

What if N is 21??

i chose E

You have to read the question carefully: "if n is a two-digit even integer..." 21 is not even.
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Manager  B
Joined: 14 Jan 2013
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Concentration: Strategy, Technology
GMAT Date: 08-01-2013
GPA: 3.7
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Re: If N is a two-digit even integer, is N < 20?  [#permalink]

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I am getting A as answer....

Not sure how C....is OA..
Manager  B
Joined: 14 Jan 2013
Posts: 127
Concentration: Strategy, Technology
GMAT Date: 08-01-2013
GPA: 3.7
WE: Consulting (Consulting)
Re: If N is a two-digit even integer, is N < 20?  [#permalink]

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Yes clear...

I did some silly mistake Thanks a lot
Intern  Joined: 08 Jan 2014
Posts: 16
Location: United States
Concentration: General Management, Entrepreneurship
GMAT Date: 06-30-2014
GPA: 3.99
WE: Analyst (Consulting)
Re: If N is a two-digit even integer, is N < 20?  [#permalink]

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Target question: Is N < 20?

Statement 1: The product of the digits of N is less than the sum of the digits of N.
Under what circumstances is the product of the digits of N less than the sum of the digits?
This occurs when one of the digits is either a 0 or a 1.
So, for example, N could equal 10, 11, 12, ....,20, 21, ...30, 31, 40, 41, 50, 51etc.
BUT the question says that N is EVEN.
So, N can be 10, 12, 14, 16, 18, 20, 30, 40, 50, 60, 70, 80, or 90
As you can see, N can be less than 20, or N can be greater than 20
Since we cannot answer the target question with certainty, statement 1 is NOT SUFFICIENT

Statement 2: The product of the digits of N is positive.
There are several possible values of N. Here are two:
Case a: N = 12 (product is less than sum). Here, N is less than 20
Case b: N = 21 (product is less than sum). Here, N is greater than 20
Since we cannot answer the target question with certainty, statement 2 is NOT SUFFICIENT

Statements 1 and 2 combined
Statement 1 tells us that N = 10, 12, 14, 16, 18, 20, 30, 40, 50, 60, 70, 80, or 90
Statement 2 lets us exclude values of N such that one of the digits is zero (since the product of the digits is zero and zero is not positive)
So, if we exclude values of N that have a zero digit, we're left with N = 12, 14, 16 or 18
This means that N is definitely less than 20
Since we can answer the target question with certainty, the combined statements are SUFFICIENT

Manager  Joined: 04 Jan 2014
Posts: 94
Re: If N is a two-digit even integer, is N < 20?  [#permalink]

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Bunuel wrote:
Mountain14 wrote:
I am getting A as answer....

Not sure how C....is OA..

(2) The product of the digits of N is positive. This implies that neither of the digits of N is zero.

Hi Bunnel

Isn't zero considered a positive integer as well?

Thanks
Math Expert V
Joined: 02 Sep 2009
Posts: 59722
Re: If N is a two-digit even integer, is N < 20?  [#permalink]

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pretzel wrote:
Bunuel wrote:
Mountain14 wrote:
I am getting A as answer....

Not sure how C....is OA..

(2) The product of the digits of N is positive. This implies that neither of the digits of N is zero.

Hi Bunnel

Isn't zero considered a positive integer as well?

Thanks

No. Zero is neither positive nor negative even integer.
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Intern  Joined: 12 Sep 2015
Posts: 3
Re: If N is a two-digit even integer, is N < 20?  [#permalink]

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Bunuel wrote:
Mountain14 wrote:
I am getting A as answer....

Not sure how C....is OA..

If N is a two-digit even integer, is N < 20?

(1) The product of the digits of N is less than the sum of the digits of N. This case is possible only if either digit is 0 or 1. For example, N can be 10, 12, 14, 16, 18, 20, 30, 40, ... So, N can be less as well as greater or equal to 20. Not sufficient.

(2) The product of the digits of N is positive. This implies that neither of the digits of N is zero. N still can be be less as well as greater than 20, for example, consider 12 or 22. Not sufficient.

(1)+(2) Since neither of the digits of N is zero, then values of N like 20, 30, 40, ... are not possible, thus N is definitely less than 20 (12, 14, 16, 18). Sufficient.

Hope it's clear.

when i started to solve the problem, i assumed one of the integers of N is negative as per statement 1. for example N has X and Y if X or Y is negative so statement 1 would be fulfilled. for example X is -2, Y is 4 ==> -2*4 = -8 while summing both of them -2+4 = 2. so statement 1 is not sufficient. statement 2 is not sufficient as well. while combining both statement it would not be sufficient. why did we neglect positive and negative number assumption?
Intern  Joined: 23 May 2016
Posts: 7
Re: If N is a two-digit even integer, is N < 20?  [#permalink]

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Hi guys,

Can someone help explain why we are not considering negative numbers here? (Product will be + which will be > the sum) so it satisfies the initial condition. if we assume negative, then 1 and 2 both dont tell us anything either?
Intern  B
Joined: 31 Aug 2016
Posts: 45
If N is a two-digit even integer, is N < 20?  [#permalink]

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Easier solution -- The correct Q indicates that N is positive!

N=10B+A with A=0, 2, 4, 6, 8

Yes -- B=1 and A=0, 2, 4, 6, 8
No -- B>=2 and A=0, 2, 4, 6, 8

(1) AB<A+B
Option 1: If B=1 then A<A+1 or 0<1 -- CHECK
Option 2: If B=2 then 2A<A+2 or A<2 therefore A can be 0 -- CHECK {or if B=5 then 5A<A+5 or A<5/4... leads to A=0}

Therefore INSUFFICIENT

(2) AB>0 or A≠0 and B≠0
A=2, 4, 6, 8 and B=1, 2, 3...

Therefore INSUFFICIENT

(1+2) The (2) cancels the Option 2 from (1) therefore SUFFICIENT!

Bunuel check
Intern  B
Joined: 21 Sep 2019
Posts: 3
Re: If N is a two-digit even integer, is N < 20?  [#permalink]

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Hi Everyone!
Can this be done with algebra?

Like... is 10t+u<20?

1) 10du<10d+u
2) 10du not 0

Thank you very much in advance!
Manu Re: If N is a two-digit even integer, is N < 20?   [#permalink] 01 Dec 2019, 12:31
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