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# M20-10

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Math Expert
Joined: 02 Sep 2009
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16 Sep 2014, 01:08
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Difficulty:

55% (hard)

Question Stats:

64% (01:09) correct 36% (01:23) wrong based on 152 sessions

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If $$N$$ is a two-digit positive integer, what is the value of its tens digit?

(1) $$2N$$ is a two-digit integer whose tens digit is 7

(2) The tens digit of $$(N - 9)$$ is 2
[Reveal] Spoiler: OA

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16 Sep 2014, 01:08
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Official Solution:

Statement (1) by itself is sufficient. $$2N$$ can be any of the five numbers: 70, 72, 74, 76, 78. In any of these cases the tens digit of $$N$$ is 3.

Statement (2) by itself is insufficient. Consider $$N = 30$$ (the answer is 3) and $$N = 29$$ (the answer is 2).

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14 Jun 2016, 09:12
I don't agree with the explanation. If the Number is 30 and you substract it by 9 you get 21 and hence the tens digit is 2; Similarly the number 29 - 9 =20 and the tens digit is 2 again
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14 Jun 2016, 09:16
parmarankita26 wrote:
I don't agree with the explanation. If the Number is 30 and you substract it by 9 you get 21 and hence the tens digit is 2; Similarly the number 29 - 9 =20 and the tens digit is 2 again

Hi,

this is exactly the reason why statement II is not sufficient alone - you should take N as initial value 30 and 29 and not the answer N-9..

The explanation also is the same so why you don't agree to it?
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Math Expert
Joined: 02 Sep 2009
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14 Jun 2016, 09:17
parmarankita26 wrote:
I don't agree with the explanation. If the Number is 30 and you substract it by 9 you get 21 and hence the tens digit is 2; Similarly the number 29 - 9 =20 and the tens digit is 2 again

We need to find tens digit of N. In one case its 3 (N=30) and in another its 2 (29).
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26 Sep 2017, 05:56
Bunuel could you solve this question mathematically
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26 Sep 2017, 11:29
If NN is a two-digit positive integer, what is the value of its tens digit?

(1) 2N is a two-digit integer whose tens digit is 7

(2) The tens digit of (N−9)(N−9) is 2

Sol-
A- As given in option A ten digit is 7,this is only possible when we have 3 as Unit digit if it is able to create one carry to ten digit(30*2=60 -34*2=6_ but from 35*2 to 39*2= 7_
With this logic ,we are left with options- 35,36,37,38,39 only. Hence,for all options,Ten digit is-3-Sufficient
B- Subtract all above choices with 9 and you will get two options as: 2_ or 30 . Insufficient
Hence, Option A
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26 Sep 2017, 19:03
2N can be any of the five numbers: 70, 72, 74, 76, 78, since the tens digit is 7 and the number is an even number (multiplied by 2). In any of these cases the tens digit of N is 3. Hence, Statement (1) by itself is sufficient.

Now from statement 2:

Consider N=30, the tens digit is 3 and for N=29 the tens digit is is 2. Hence, Insufficient

Re: M20-10   [#permalink] 26 Sep 2017, 19:03
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# M20-10

Moderators: chetan2u, Bunuel

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