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16 Sep 2014, 01:18
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If \(z\) is a three-digit positive integer, what is the tens digit of \(z\) ?
(1) The tens digit of \((z - 91)\) is 3
(2) The units digit of \((z + 9)\) is 5
(1) The tens digit of \((z - 91)\) is 3
(2) The units digit of \((z + 9)\) is 5
16 Sep 2014, 01:18
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Official Solution:
If \(z\) is a three-digit positive integer, what is the tens digit of \(z\) ?
(1) The tens digit of \(z - 91\) is 3.
If \(z-91=130\), then \(z=130+91=221\) and the tens digit of \(z\) is 2.;
If \(z-91=139\), then \(z=139+91=230\) and the tens digit of \(z\) is 3..
Two different answers, hence this statement is not sufficient.
(2) The units digit of \(z + 9\) is 5.
From this information, we can determine that the units digit of \(z\) is 6. However, the tens digit of \(z\) could be any digit between 0 and 9. If \(z+9=115\), then \(z=115-9=106\) and the tens digit of \(z\) is 0.;
If \(z+9=125\), then \(z=125-9=116\) and the tens digit of \(z\) is 1. .
Two different answers, hence this statement is not sufficient.
(1)+(2) From (1) we know that \(z\) is the sum of a number with a tens digit of 3 and 91 and from (2) we know that the units digit of \(z\) is 6.
?3?
+91
??6
In order for the sum to have a units digit of 6, the units digit of the first number must be 5. Hence:
?35
+91
?26
Therefore, the tens digit of \(z\) is 2. Sufficient.
Answer: C
If \(z\) is a three-digit positive integer, what is the tens digit of \(z\) ?
(1) The tens digit of \(z - 91\) is 3.
If \(z-91=130\), then \(z=130+91=221\) and the tens digit of \(z\) is 2.;
If \(z-91=139\), then \(z=139+91=230\) and the tens digit of \(z\) is 3..
Two different answers, hence this statement is not sufficient.
(2) The units digit of \(z + 9\) is 5.
From this information, we can determine that the units digit of \(z\) is 6. However, the tens digit of \(z\) could be any digit between 0 and 9. If \(z+9=115\), then \(z=115-9=106\) and the tens digit of \(z\) is 0.;
If \(z+9=125\), then \(z=125-9=116\) and the tens digit of \(z\) is 1. .
Two different answers, hence this statement is not sufficient.
(1)+(2) From (1) we know that \(z\) is the sum of a number with a tens digit of 3 and 91 and from (2) we know that the units digit of \(z\) is 6.
?3?
+91
??6
In order for the sum to have a units digit of 6, the units digit of the first number must be 5. Hence:
?35
+91
?26
Answer: C
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02 Jun 2021, 19:57
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I think this is a high-quality question and I agree with the explanation
