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If N is a 3-digit integer, what is the value of N?

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Amrita2405
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If N is a 3-digit integer, what is the value of N? [#permalink] New post   12 Apr 2019, 23:37
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If N is a 3-digit integer, what is the value of N?

(1) The ten’s digit of N is twice the unit’s digit and half of the hundred’s digit.
(2) The ten’s digit of N is thrice the unit’s digit and one-third of the hundred’s digit.
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Re: If N is a 3-digit integer, what is the value of N? [#permalink] New post   13 Apr 2019, 00:59
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Amrita2405 wrote:
If N is a 3-digit integer, what is the value of N?

(1) The ten’s digit of N is twice the unit’s digit and half of the hundred’s digit.
(2) The ten’s digit of N is thrice the unit’s digit and one-third of the hundred’s digit.


Let the 3 digit integer, N, be HTO.

1. H = 4x, T = 2x, O = x
Case 1: x = 1, the three digit integer is 421.
Case 2: x = 2, the three digit integer is 842.
Since we have two different integers, we don't have an unique value of N. (Insufficient)

2. H = 9x, T = 3x, O = x
When x = 1, the three digit integer is 931.
This is the only option as N is not a 3-digit number when x = 2. (Sufficient - Option B)
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Re: If N is a 3-digit integer, what is the value of N? [#permalink] New post   12 Apr 2019, 23:48
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1. has 2 possibilities (421 and 842) so it is insufficient on it's own.

2. Has only 1 possibility (931) so we know that N is definitely 931, making this statement sufficient on it's own.

B it is.

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If N is a 3-digit integer, what is the value of N? [#permalink] New post   13 Apr 2019, 06:01
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neha283

If you consider one of the digits to be 0 - all the three digits must be 0. N will cease to be a 3 digit integer. That's the reason 0 isint considered.
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Re: If N is a 3-digit integer, what is the value of N? [#permalink] New post   13 Apr 2019, 07:31
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neha283 wrote:
pushpitkc wrote:
Amrita2405 wrote:
If N is a 3-digit integer, what is the value of N?

(1) The ten’s digit of N is twice the unit’s digit and half of the hundred’s digit.
(2) The ten’s digit of N is thrice the unit’s digit and one-third of the hundred’s digit.


Let the 3 digit integer, N, be HTO.

1. H = 4x, T = 2x, O = x
Case 1: x = 1, the three digit integer is 421.
Case 2: x = 2, the three digit integer is 842.
Since we have two different integers, we don't have an unique value of N. (Insufficient)

2. H = 9x, T = 3x, O = x
When x = 1, the three digit integer is 931.
This is the only option as N is not a 3-digit number when x = 2. (Sufficient - Option B)


I was wondering why are we not considering 0 in tens and units digits? that may open another set of possible combinations.


If you consider tens digit as 0 then how will the first condition be true? Lets say XYZ is your 3 digit number

If Y=0, X=0/2= which is undefined

Similarly if you put units digit as 0, it wont make sense

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Re: If N is a 3-digit integer, what is the value of N? [#permalink] New post   13 Apr 2019, 05:54
pushpitkc wrote:
Amrita2405 wrote:
If N is a 3-digit integer, what is the value of N?

(1) The ten’s digit of N is twice the unit’s digit and half of the hundred’s digit.
(2) The ten’s digit of N is thrice the unit’s digit and one-third of the hundred’s digit.


Let the 3 digit integer, N, be HTO.

1. H = 4x, T = 2x, O = x
Case 1: x = 1, the three digit integer is 421.
Case 2: x = 2, the three digit integer is 842.
Since we have two different integers, we don't have an unique value of N. (Insufficient)

2. H = 9x, T = 3x, O = x
When x = 1, the three digit integer is 931.
This is the only option as N is not a 3-digit number when x = 2. (Sufficient - Option B)


I was wondering why are we not considering 0 in tens and units digits? that may open another set of possible combinations.
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neha283
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Re: If N is a 3-digit integer, what is the value of N? [#permalink] New post   13 Apr 2019, 07:41
I was wondering why are we not considering 0 in tens and units digits? that may open another set of possible combinations.[/quote]

If you consider tens digit as 0 then how will the first condition be true? Lets say XYZ is your 3 digit number

If Y=0, X=0/2= which is undefined

Similarly if you put units digit as 0, it wont make sense

Posted from my mobile device[/quote]

Yep, got it. Silly one. Thanks mate! :)
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Re: If N is a 3-digit integer, what is the value of N? [#permalink] New post   13 Apr 2019, 07:51
neha283 wrote:
I was wondering why are we not considering 0 in tens and units digits? that may open another set of possible combinations.


If you consider tens digit as 0 then how will the first condition be true? Lets say XYZ is your 3 digit number

If Y=0, X=0/2= which is undefined

Similarly if you put units digit as 0, it wont make sense

Posted from my mobile device[/quote]

Yep, got it. Silly one. Thanks mate! :)[/quote]

Dont worry! Happens to the best of us!

Instead of thanks, you can just give kudos! Its faster :))
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Re: If N is a 3-digit integer, what is the value of N? [#permalink] New post   21 Jan 2022, 07:02
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Re: If N is a 3-digit integer, what is the value of N? [#permalink]
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