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Which of the following cannot be the sum of a two-digit number and the
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09 Feb 2022, 07:30
09 Feb 2022, 07:30
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Which of the following cannot be the sum of a two-digit number and the number obtained by reversing the two digits?
(A) 88
(B) 121
(C) 134
(D) 143
(E) 187
(A) 88
(B) 121
(C) 134
(D) 143
(E) 187
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Re: Which of the following cannot be the sum of a two-digit number and the
[#permalink]
10 Feb 2022, 07:44
10 Feb 2022, 07:44
1
Carcass wrote:
Which of the following cannot be the sum of a two-digit number and the number obtained by reversing the two digits?
(A) 88
(B) 121
(C) 134
(D) 145
(E) 187
(A) 88
(B) 121
(C) 134
(D) 145
(E) 187
Let a and b represent the tens digit and units digit of the original number, respectively.
So, the VALUE of the original number = 10a + b (in the same way that 37 = (10)(3) + 7)
When we reverse the digits, a now represents the units digit, and b represents the tens digit.
So, the VALUE of the reversed number = 10b + a
So, the SUM of the two numbers = (10a + b) + (10b + a) = 11a + 11b = 11(a +b)
This tells us that the sum of the two numbers must be a multiple of 11
Let me check the other choices we see that answer choice C (134) is NOT a multiple of 11
Answer: C
Re: Which of the following cannot be the sum of a two-digit number and the
[#permalink]
05 Aug 2022, 23:42
05 Aug 2022, 23:42
1
Carcass, the options for the given question require a second look as 145 and 134 are both not divisible by 11. So there is no one option to be chosen as the correct answer.
