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

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Bunuel
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Which of the following pairs of numbers (x,y) is NOT a valid solutio [#permalink] New post   08 Oct 2017, 06:33
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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)
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C
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Which of the following pairs of numbers (x,y) is NOT a valid solutio [#permalink] New post   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)

This looked like a monster problem. Then I saw the key: 5920. Its units digit is 0.

Thus the second term (5920*y) in every answer will end in 0:
(---0 * anything) = last digit of 0
y doesn't matter.
The second term can be written (---0)

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

The first number, 8933, ends in 3.
It will be multiplied by x.
And the product of (3*x) must end in 7
because 97 ends with 7: _7

We subtract the second number's last digit of 0 from the last digit of (3*x).

(Product of 3*x) - (----0) = _7
(---7) - (----0) = _7

So check only the first term in the options.
(3 * x) must = _7

If (3 * x) must end in 7, then
the units digit of x must be 9.
(3*1)=3. (3*2)=6 ... Only (3*9)=27 works.
(---3)*(9) = ----7

All the answers except (C) end in 9.

Check C if you want to be sure
If x were (C), it would yield (16588 * 8933) = nnnn4
\((4 - 0)\neq{7}\)
(first term) - (second term) cannot = 97
Not a valid solution.


Answer C
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manik919
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Re: Which of the following pairs of numbers (x,y) is NOT a valid solutio [#permalink] New post   08 Oct 2017, 07:06
Ans. C
8933*16588-5920*25031
4-0=4 (multiplying only the unit digits to get an idea)
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Re: Which of the following pairs of numbers (x,y) is NOT a valid solutio [#permalink] New post   12 Oct 2017, 01:26
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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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Re: Which of the following pairs of numbers (x,y) is NOT a valid solutio [#permalink] New post   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

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


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.

Answer: C
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Re: Which of the following pairs of numbers (x,y) is NOT a valid solutio [#permalink] New post   04 May 2019, 00:21
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)


8933*x-5920*y=97
As we can see,the result is an odd number
The product of 8933*x can be either an odd number or even, while 5920*y is always even
To get an odd number 8933*x Must be an odd number ( ODD-EVEN=ODD)

We search for numbers which makes 8933*x even. Only C makes the product even

I hope this is helpful!
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Re: Which of the following pairs of numbers (x,y) is NOT a valid solutio [#permalink] New post   15 May 2019, 03:45
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)



8933x − 5920y = 97

97 is odd integer.

5920y = even

8933x must be odd.

Thus x must be odd.

C is the correct answer.
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Which of the following pairs of numbers (x,y) is NOT a valid solutio [#permalink] New post   15 May 2019, 04:36
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)


Let us consider all the lat digits of Option C

3*8 - 0*1 = 7, not possible. It has to be 4.
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Re: Which of the following pairs of numbers (x,y) is NOT a valid solutio [#permalink] New post   20 May 2019, 19:07
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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)



We see that coefficients of the given equation 8933x − 5920y = 97 and the coordinates in the given choices are big numbers. So we will analyze them using units digits only.

A) (4749, 7166)
Since 3(9) - 0(6) = 27 has a units digit of 7, the coordinates in choice A can be a solution.

B) (10669, 16099)

Since 3(9) - 0(9) = 27 has a units digit of 7, the coordinates in choice B can be a solution.

C) (16588, 25031)

Since 3(8) - 0(1) = 24 has a units digit of 4 but we need a units digit of 7, the coordinates in choice C CAN’T be a solution.

Answer: C
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Re: Which of the following pairs of numbers (x,y) is NOT a valid solutio [#permalink] New post   10 Jan 2022, 05:44
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Re: Which of the following pairs of numbers (x,y) is NOT a valid solutio [#permalink]
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