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# xx is a two digit integer, the first term of a sequence of consecutive

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VP
Joined: 07 Dec 2014
Posts: 1153
xx is a two digit integer, the first term of a sequence of consecutive  [#permalink]

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03 Dec 2017, 19:50
5
00:00

Difficulty:

55% (hard)

Question Stats:

77% (03:00) correct 23% (03:05) wrong based on 44 sessions

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xx is a two digit integer, the first term of a sequence of consecutive odd positive integers. If the sum of xx and the last term equals 100, and the product of xx and the last term is a number whose four digits equal, in order, x-1, x-1, x-2, x-2, then what is the sum of the four digits?

A. 6
B. 10
C. 14
D. 18
E. 22
Senior Manager
Joined: 17 Oct 2016
Posts: 318
Location: India
Concentration: Operations, Strategy
GPA: 3.73
WE: Design (Real Estate)
Re: xx is a two digit integer, the first term of a sequence of consecutive  [#permalink]

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03 Dec 2017, 20:02
Based on the given criteria the only two possibilities are 11 and 33.

When it’s 11 the last digit has to be 89. In this case the product is 11*89=979 which is not a four digit number.

For 33 the last digit has to be 67 and their product is 2211 which meets the given criteria. Hence the answer has to be 2+2+1+1=6

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SVP
Joined: 12 Dec 2016
Posts: 1600
Location: United States
GMAT 1: 700 Q49 V33
GPA: 3.64
Re: xx is a two digit integer, the first term of a sequence of consecutive  [#permalink]

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03 Dec 2017, 23:45
gracie wrote:
xx is a two digit integer, the first term of a sequence of consecutive odd positive integers. If the sum of xx and the last term equals 100, and the product of xx and the last term is a number whose four digits equal, in order, x-1, x-1, x-2, x-2, then what is the sum of the four digits?

A. 6
B. 10
C. 14
D. 18
E. 22

can you name the source, pls?
I think this question is interesting, but I do not know the real test will like this question.
VP
Joined: 07 Dec 2014
Posts: 1153
Re: xx is a two digit integer, the first term of a sequence of consecutive  [#permalink]

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04 Dec 2017, 09:35
1
chesstitans wrote:
gracie wrote:
xx is a two digit integer, the first term of a sequence of consecutive odd positive integers. If the sum of xx and the last term equals 100, and the product of xx and the last term is a number whose four digits equal, in order, x-1, x-1, x-2, x-2, then what is the sum of the four digits?

A. 6
B. 10
C. 14
D. 18
E. 22

can you name the source, pls?
I think this question is interesting, but I do not know the real test will like this question.

hi chesstitans,
gracie
Intern
Joined: 29 Nov 2017
Posts: 1
Re: xx is a two digit integer, the first term of a sequence of consecutive  [#permalink]

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04 Dec 2017, 10:26
Sasindran wrote:
Based on the given criteria the only two possibilities are 11 and 33.

When it’s 11 the last digit has to be 89. In this case the product is 11*89=979 which is not a four digit number.

For 33 the last digit has to be 67 and their product is 2211 which meets the given criteria. Hence the answer has to be 2+2+1+1=6

Posted from my mobile device

Or maybe I can't translate it correctly...
VP
Joined: 07 Dec 2014
Posts: 1153
Re: xx is a two digit integer, the first term of a sequence of consecutive  [#permalink]

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04 Dec 2017, 12:39
TTania wrote:
Sasindran wrote:
Based on the given criteria the only two possibilities are 11 and 33.

When it’s 11 the last digit has to be 89. In this case the product is 11*89=979 which is not a four digit number.

For 33 the last digit has to be 67 and their product is 2211 which meets the given criteria. Hence the answer has to be 2+2+1+1=6

Posted from my mobile device

Or maybe I can't translate it correctly...

hi TTania,
we know that xx is an odd two digit number with identical digits, less than the sequence mean/median of 50
11 is not a possibility because x-1 and x-2 would then have a zero or negative value
33 is the only choice
I hope this helps,
gracie
Re: xx is a two digit integer, the first term of a sequence of consecutive &nbs [#permalink] 04 Dec 2017, 12:39
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