The integer x has a tens digit of 6 and a units digit of 7. The units digit of integer y is 8. The product of x and y has a tens digit of 8. Which of the following is a possible tens digit of integer y?
A. 3
B. 4
C. 5
D. 6
E. 7
OA C
Source: Veritas Prep
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The integer x has a tens digit of 6 and a units digit of 7. The units digit of integer y is 8. The product of x and y
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BTGmoderatorDC
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We can try as follows:BTGmoderatorDC wrote: ↑Tue Nov 03, 2020 5:55 pmThe integer x has a tens digit of 6 and a units digit of 7. The units digit of integer y is 8. The product of x and y has a tens digit of 8. Which of the following is a possible tens digit of integer y?
A. 3
B. 4
C. 5
D. 6
E. 7
OA C
Source: Veritas Prep
\(x=67\)
\(y=p8\)
Multiplying them, we have \((10p+8)\cdot 67 \Rightarrow 670p+536\)
Now, checking values
\(p=3 \Rightarrow\) Tens digit of the result \(=4 \Large{\color{red}\chi}\)
\(p=4 \Rightarrow\) Tens digit of the result \(=1 \Large{\color{red}\chi}\)
\(p=5 \Rightarrow\) Tens digit of the result \(=8 \Large{\color{green}\checkmark}\)
Therefore, C
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Solution:BTGmoderatorDC wrote: ↑Tue Nov 03, 2020 5:55 pmThe integer x has a tens digit of 6 and a units digit of 7. The units digit of integer y is 8. The product of x and y has a tens digit of 8. Which of the following is a possible tens digit of integer y?
A. 3
B. 4
C. 5
D. 6
E. 7
OA C
We see that a possible value of integer x is 67. If we let the tens digit of y be t, then 10t + 8 is one of the possible value of y, and the product of xy is:
67(10t + 8) = 670t + 536 = 600t + 70t + 500 + 30 + 6 = 100(6t + 5) + 10(7t + 3) + 6
The tens digit of xy is the units digit of the value 7t + 3 and it should be 8. Now let’s check the given answer choices:
A) 7(3) + 3 = 24 → The units digit is not 8.
B) 7(4) + 3 = 31 → The units digit is not 8.
C) 7(5) + 3 = 38 → The units digit IS 8.
Answer: C
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