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

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Director
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xx is a two digit integer, the first term of a sequence of consecutive [#permalink]

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69% (02:20) correct 31% (24:20) wrong based on 26 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
[Reveal] Spoiler: OA

Kudos [?]: 291 [1], given: 16

Manager
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S
Joined: 17 Oct 2016
Posts: 148

Kudos [?]: 38 [0], given: 89

Location: India
Concentration: Operations, Strategy
GPA: 3.7
WE: Design (Real Estate)
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Re: xx is a two digit integer, the first term of a sequence of consecutive [#permalink]

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New post 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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Help with kudos if u found the post useful. Thanks

Kudos [?]: 38 [0], given: 89

VP
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S
Joined: 12 Dec 2016
Posts: 1343

Kudos [?]: 46 [0], given: 1366

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

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New post 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.

Kudos [?]: 46 [0], given: 1366

1 KUDOS received
Director
Director
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G
Joined: 07 Dec 2014
Posts: 859

Kudos [?]: 291 [1], given: 16

Re: xx is a two digit integer, the first term of a sequence of consecutive [#permalink]

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New post 04 Dec 2017, 09:35
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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,
I made it up.
gracie

Kudos [?]: 291 [1], given: 16

Intern
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Joined: 29 Nov 2017
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Kudos [?]: 0 [0], given: 1

Re: xx is a two digit integer, the first term of a sequence of consecutive [#permalink]

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New post 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


Please help me to understand the mechanics, how did you get 33?
Or maybe I can't translate it correctly...

Kudos [?]: 0 [0], given: 1

Director
Director
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G
Joined: 07 Dec 2014
Posts: 859

Kudos [?]: 291 [0], given: 16

Re: xx is a two digit integer, the first term of a sequence of consecutive [#permalink]

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New post 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


Please help me to understand the mechanics, how did you get 33?
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

Kudos [?]: 291 [0], given: 16

Re: xx is a two digit integer, the first term of a sequence of consecutive   [#permalink] 04 Dec 2017, 12:39
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