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# If 1 < p < 2, is the tenths’ digit of the decimal representation of p

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Joined: 02 Sep 2009
Posts: 52294
If 1 < p < 2, is the tenths’ digit of the decimal representation of p  [#permalink]

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21 Sep 2018, 00:42
00:00

Difficulty:

35% (medium)

Question Stats:

70% (01:20) correct 30% (01:28) wrong based on 69 sessions

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If 1 < p < 2, is the tenths’ digit of the decimal representation of p equal to 9?

(1) p + 0.01 < 2
(2) p + 0.1 > 2

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Re: If 1 < p < 2, is the tenths’ digit of the decimal representation of p  [#permalink]

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21 Sep 2018, 00:51
1
Bunuel wrote:
If 1 < p < 2, is the tenths’ digit of the decimal representation of p equal to 9?

(1) p + 0.01 < 2
(2) p + 0.1 > 2

For a number abc.def
a = Unit's Digit
b = Tens Digit
c = Hundreds Digit
d = tenth's Digit
e = Hundredth Digit
f = Thousandths digit

Question: If 1 < p < 2, is the tenths’ digit of the decimal representation of p equal to 9?

Statement 1: p + 0.01 < 2
@p = 1.1, p + 0.01 = 1.11 NO
@p=1.9, p + 0.01 = 1.91 YES

NOT SUFFICIENT

Statement 2: p + 0.1 > 2

i.e. p > 1.9 and also p < 2
i.e. 1.9 < p < 2
i.e. tenth digit of p must be 9 hence

SUFFICIENT

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Re: If 1 < p < 2, is the tenths’ digit of the decimal representation of p  [#permalink]

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21 Sep 2018, 00:54
From statement 1:

p+0.01<2
p<1.99
P can be any value between 1 to 2.
So, decimal value may or might not be equal.
1 is insufficient.

From statement 2:

p+0.1>2
p>1.9
So, tenths’ digit of the decimal representation of p equal to 9
2 is sufficient.

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Re: If 1 < p < 2, is the tenths’ digit of the decimal representation of p  [#permalink]

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21 Sep 2018, 04:57
Top Contributor
Bunuel wrote:
If 1 < p < 2, is the tenths’ digit of the decimal representation of p equal to 9?

(1) p + 0.01 < 2
(2) p + 0.1 > 2

Target question: Is the tenths digit of p equal to 9?

Given: 1 < p < 2

Statement 1: p + 0.01 < 2
Subtract 0.01 from both sides of the inequality to get: p < 1.99
We also know that 1 < p < 2
So, we can now conclude that 1 < p < 1.99
There are several values of p that satisfy statement 1. Here are two:
Case a: p = 1.5, in which case, the answer to the target question is the tenths digit is 5
Case b: p = 1.4, in which case, the answer to the target question is the tenths digit is 4
Since we cannot answer the target question with certainty, statement 1 is NOT SUFFICIENT

Statement 2: p + 0.1 > 2
Subtract 0.01 from both sides of the inequality to get: p > 1.9
We also know that 1 < p < 2
So, we can now conclude that 1.9 < p < 2
If p is greater than 1.9 and less than 2, then p = 1.9something
In other words, the answer to the target question is the tenths digit is 9
Since we can answer the target question with certainty, statement 2 is SUFFICIENT

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Re: If 1 < p < 2, is the tenths’ digit of the decimal representation of p &nbs [#permalink] 21 Sep 2018, 04:57
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