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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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New post 07 Feb 2018, 08:15
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Question Stats:

46% (02:18) correct 54% (02:18) wrong based on 39 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
[Reveal] Spoiler: OA

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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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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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New post 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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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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New post 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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