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# Which of the following pairs of numbers (x,y) is NOT a valid solutio

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Math Expert
Joined: 02 Sep 2009
Posts: 42247

Kudos [?]: 132657 [0], given: 12331

Which of the following pairs of numbers (x,y) is NOT a valid solutio [#permalink]

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08 Oct 2017, 06:33
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Question Stats:

73% (01:01) correct 27% (02:10) wrong based on 75 sessions

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Which of the following pairs of numbers (x,y) is NOT a valid solution to the equation 8933x − 5920y = 97?

A. (4749, 7166)
B. (10669, 16099)
C. (16588, 25031)
D. (22509, 33965)
E. (28429, 42898)
[Reveal] Spoiler: OA

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Kudos [?]: 132657 [0], given: 12331

Intern
Joined: 16 Jul 2016
Posts: 12

Kudos [?]: 2 [0], given: 28

Re: Which of the following pairs of numbers (x,y) is NOT a valid solutio [#permalink]

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08 Oct 2017, 07:06
Ans. C
8933*16588-5920*25031
4-0=4 (multiplying only the unit digits to get an idea)

Kudos [?]: 2 [0], given: 28

Director
Joined: 22 May 2016
Posts: 979

Kudos [?]: 337 [1], given: 591

Which of the following pairs of numbers (x,y) is NOT a valid solutio [#permalink]

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08 Oct 2017, 10:07
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Bunuel wrote:
Which of the following pairs of numbers (x,y) is NOT a valid solution to the equation 8933x − 5920y = 97?

A. (4749, 7166)
B. (10669, 16099)
C. (16588, 25031)
D. (22509, 33965)
E. (28429, 42898)

At first I thought this was a monster problem. Then I saw the key: 5920. Its units digit is 0.

Thus second term will end in 0: (---0 * anything) = last digit of 0. y doesn't matter.

So: (--3)x - (--0) = 7

The first term, after multiplication by x, must end in 7. (--7) - (--0) = 7

Check only the x term in the options. (3 * x) must = 7. Units digit of x must be 9.
(---3)*(9) = ---7

All the answers except (C) end in 9.

If x were (C), it would yield 16588 * 8933 = nnnn4. $$(4 - 0)\neq{7}$$

Kudos [?]: 337 [1], given: 591

Intern
Joined: 01 Feb 2017
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Kudos [?]: 18 [0], given: 19

Re: Which of the following pairs of numbers (x,y) is NOT a valid solutio [#permalink]

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12 Oct 2017, 01:26
8933x-5920y=97

For this equation to be valid:
1. x<y as (8933-5920)>97. So, we need to reduce the LHS value.

2. 8933x must be an Odd number because 5920y is an even number and 97 is an odd number.
That means, value of x cannot be an even number.

Hence, Ans C is the only option with x as even

Therefore, Ans C

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Kudos [?]: 18 [0], given: 19

Intern
Joined: 29 Aug 2010
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Kudos [?]: 9 [0], given: 124

Re: Which of the following pairs of numbers (x,y) is NOT a valid solutio [#permalink]

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14 Oct 2017, 09:15
8933x-5920y=97

If we don't get the units digit 7 after multiplying by x, then we got the answer:

A. (4749, 7166) ----> ...3* ...9= ....7 May be Valid
B. (10669, 16099)---> ....3*....9= ....7 May be Valid
C. (16588, 25031)---> ....3*....8= ....4 Not Valid hence Answer
D. (22509, 33965)---> ....3*....9= ....7 May be Valid
E. (28429, 42898)---> ....3*....9= ....7 May be Valid

If you like my approach, hit [u]+1Kudos button

Kudos [?]: 9 [0], given: 124

Target Test Prep Representative
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Re: Which of the following pairs of numbers (x,y) is NOT a valid solutio [#permalink]

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16 Oct 2017, 16:49
Bunuel wrote:
Which of the following pairs of numbers (x,y) is NOT a valid solution to the equation 8933x − 5920y = 97?

A. (4749, 7166)
B. (10669, 16099)
C. (16588, 25031)
D. (22509, 33965)
E. (28429, 42898)

We can solve this problem using units digits.

We see that the product of 5920 and y will always have a units digit of zero, since the product of any number and a number with a units digit of zero must end in a zero.

Thus, we see that the product of 8933 and x must have a units digit of 7, since 8933x − 5920y = 97.

Of our answer choices, we see that answer choices A, B, D, and E have units digits of 9 for the value of x. Answer choice C is the one that doesn’t have a units digit of 9. Since we are looking for the one that is NOT a valid solution, choice C must be the one that is NOT valid.

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Jeffery Miller

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Kudos [?]: 902 [0], given: 5

Re: Which of the following pairs of numbers (x,y) is NOT a valid solutio   [#permalink] 16 Oct 2017, 16:49
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