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# If a and b are two-digit positive numbers and c is a three digit posit

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If a and b are two-digit positive numbers and c is a three digit posit  [#permalink]

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Updated on: 07 Feb 2018, 10:39
5
00:00

Difficulty:

75% (hard)

Question Stats:

51% (02:15) correct 49% (02:32) wrong based on 64 sessions

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If a and b are two-digit positive numbers and c is a three digit positive number, such that c=a+b. Is the unit digit of c the same as the unit digit of a?

1) All the digits of c are the same and all the digits of a are the same

2) The tens digit of a is the same as the tens digit of b

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Originally posted by Teerex on 07 Feb 2018, 08:15.
Last edited by Teerex on 07 Feb 2018, 10:39, edited 1 time in total.
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Re: If a and b are two-digit positive numbers and c is a three digit posit  [#permalink]

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07 Feb 2018, 09:48
1
Teerex wrote:
If a and b are two-digit positive numbers and c is a three digit positive number, such that c=a+b, is the unit digit of the same as the unit digit of a?

1) All the digits of C are the same and all the digits of a are the same

2) The tens digit of a is the same as the tens digit of b

Hi Teerex,

I suppose the question stem is incomplete in the highlighted part above
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Re: If a and b are two-digit positive numbers and c is a three digit posit  [#permalink]

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07 Feb 2018, 10:40
pushpitkc wrote:
Teerex wrote:
If a and b are two-digit positive numbers and c is a three digit positive number, such that c=a+b, is the unit digit of the same as the unit digit of a?

1) All the digits of C are the same and all the digits of a are the same

2) The tens digit of a is the same as the tens digit of b

Hi Teerex,

I suppose the question stem is incomplete in the highlighted part above

Oops, my bad! Question has been modified. Thanks. +1
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If a and b are two-digit positive numbers and c is a three digit posit  [#permalink]

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07 Feb 2018, 10:59
1
1
Teerex wrote:
If a and b are two-digit positive numbers and c is a three digit positive number, such that c=a+b. Is the unit digit of c the same as the unit digit of a?

1) All the digits of c are the same and all the digits of a are the same

2) The tens digit of a is the same as the tens digit of b

As $$c$$ is sum of two-digit numbers so the hundred's digit of $$c$$ will be $$1$$ (max possible value $$99+99=198$$)

Statement 1: implies $$c=111$$. $$a$$ cannot be $$11$$ because in this case no value of $$b$$ will add up to $$111$$

so for unit's digit of $$c$$ to be $$1$$, unit digit pairs of $$a$$ & $$b$$ can be (2,9),(3,8),(4,7),(5,6) etc.

Hence unit's digit of $$a$$ is not equal to unit's digit of $$c$$. Sufficient

Statement 2: nothing mentioned about $$c$$. Insufficient

Option A
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If a and b are two-digit positive numbers and c is a three digit posit  [#permalink]

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13 Feb 2018, 03:03
Teerex wrote:
If a and b are two-digit positive numbers and c is a three digit positive number, such that c=a+b. Is the unit digit of c the same as the unit digit of a?

1) All the digits of c are the same and all the digits of a are the same

2) The tens digit of a is the same as the tens digit of b

Let $$a = mn, b = pq, c = rst.$$

Statement I:

$$111t = 11n + 10p + q$$.
Suppose, t = n
we get - $$100t = 10p+ q$$ ------------- This case is not possible as p,q are single digit.
Hence, t is not equal to n.

Statement II:

We get, $$100r + 10s + t = 20m + q + n.$$
Nothing can be decided on this. Insufficient.
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If a and b are two-digit positive numbers and c is a three digit posit   [#permalink] 13 Feb 2018, 03:03
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