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Manager  Joined: 28 Jan 2006
Posts: 114
In the number 1.4ab5, a and b represent single positive  [#permalink]

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29 00:00

Difficulty:   55% (hard)

Question Stats: 68% (02:12) correct 32% (02:13) wrong based on 765 sessions

### HideShow timer Statistics In the number 1.4ab5, a and b represent single positive digits. If x = 1.4ab5, what is the value of 10 – x?

(1) If x is rounded to the nearest hundredth, then 10 – x = 8.56.
(2) If x is rounded to the nearest thousandth, then 10 – x = 8.564.

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shinewine

Originally posted by shinewine on 28 Aug 2006, 15:12.
Last edited by Bunuel on 11 Jul 2013, 09:14, edited 1 time in total.
Edited the question and added the OA
Math Expert V
Joined: 02 Sep 2009
Posts: 56256
In the number 1.4ab5, a and b represent single positive  [#permalink]

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5
11
fozzzy wrote:
What's the OA for this question?

In the number 1.4ab5, a and b represent single positive digits. If x = 1.4ab5, what is the value of 10 – x?

Given: $$x = 1.4ab5$$.
Notice that we need to find the values of a and b.

(1) If x is rounded to the nearest hundredth, then 10 – x = 8.56 --> x rounded to the nearest hundredth is 1.44, which implies that $$a$$ can be 3 if $$b\geq{5}$$ or 4 if $$b<{5}$$. Not sufficient.

(2) If x is rounded to the nearest thousandth, then 10 – x = 8.564 --> x rounded to the nearest thousandth is 1.436. So, $$a=3$$ and $$b=5$$ (since the ten-thousandths digit is 5, then thousandths digit is rounded up, thus b is 1 less than 6, so 5). Sufficient.

Rounding rules

Rounding is simplifying a number to a certain place value. To round the decimal drop the extra decimal places, and if the first dropped digit is 5 or greater, round up the last digit that you keep. If the first dropped digit is 4 or smaller, round down (keep the same) the last digit that you keep.

Example:
5.3485 rounded to the nearest tenth = 5.3, since the dropped 4 is less than 5.
5.3485 rounded to the nearest hundredth = 5.35, since the dropped 8 is greater than 5.
5.3485 rounded to the nearest thousandth = 5.349, since the dropped 5 is equal to 5.

Place Values Hope it helps.

Attachment: Place Values.png [ 38.87 KiB | Viewed 11941 times ]

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##### General Discussion
Manager  Joined: 31 Jul 2006
Posts: 203

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1
It is B.

A gives 1.44. So x can be 1.4395 or 1.4415 - INSUFF

B gives 1.436. So x will be 1.43b5. Since, x is rounded to thousandth place then b has to be 5 in order to get x as 1.436. Thus, x is 1.4355. - SUFF

hence B.
Manager  Joined: 28 Jan 2006
Posts: 114

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2
gmatcrook wrote:
It is B.

A gives 1.44. So x can be 1.4395 or 1.4415 - INSUFF

B gives 1.436. So x will be 1.43b5. Since, x is rounded to thousandth place then b has to be 5 in order to get x as 1.436. Thus, x is 1.4355. - SUFF

hence B.

i am getting 2 answers for statement B>
we can get 1.436 under 2 circumstances
1> when b=6
This is because according to teh rules of rounding of.. if 5 is preceded by an even no.,we don't have to increment ..
2> whn b=5.. but when 5 is preceded by an odd no. , we need to increment.

used this link to understand rounding off..
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shinewine
Director  Joined: 28 Dec 2005
Posts: 673

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B for me

From 1:
x = 1.44
a could be 3 or 4 depending on b, also b is unknown...insuff

From 2:
x = 1.436 after rounding. clearly a is 3. b is 5 since after rounding it became 6.. we know both a and b...suff
Manager  Joined: 28 Jan 2006
Posts: 114

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GMATT73 wrote:
(B) has to be it: 1.4355

i am getting 2 answers for statement B>
we can get 1.436 under 2 circumstances
1> when b=6
This is because according to teh rules of rounding of.. if 5 is preceded by an even no.,we don't have to increment ..
2> whn b=5.. but when 5 is preceded by an odd no. , we need to increment.
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shinewine
Director  Joined: 29 Nov 2012
Posts: 731
Re: In the number 1.4ab5, a and b represent single positive  [#permalink]

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What's the OA for this question?
Math Revolution GMAT Instructor V
Joined: 16 Aug 2015
Posts: 7603
GMAT 1: 760 Q51 V42 GPA: 3.82
Re: In the number 1.4ab5, a and b represent single positive  [#permalink]

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Forget conventional ways of solving math questions. In DS, Variable approach is the easiest and quickest way to find the answer without actually solving the problem. Remember equal number of variables and independent equations ensures a solution.

In the number 1.4ab5, a and b represent single positive digits. If x = 1.4ab5, what is the value of 10 – x?

(1) If x is rounded to the nearest hundredth, then 10 – x = 8.56.
(2) If x is rounded to the nearest thousandth, then 10 – x = 8.564.

In the original condition there are 3 variables (x,a,b) and one equation (x=1.4ab5); 2 more equations are given from the conditions, so there is high chance (C) will be our answer.
If we look at the conditions together,
BY 1) 10-1.4ab5=8.56, BY 2) 10-1.4ab5=8.564, we get a=3, b=6, and the answer becomes (C). But this is a commonly made mistake;
if we look at them separately,
for condition 1, it is insufficient as x=1.4365, 1.4375
for condition 2, x=1.4365. This is sufficient, and the answer becomes (B).

For cases where we need 2 more equation, such as original conditions with “2 variables”, or “3 variables and 1 equation”, or “4 variables and 2 equations”, we have 1 equation each in both 1) and 2). Therefore, there is 70% chance that C is the answer, while E has 25% chance. These two are the majority. In case of common mistake type 3,4, the answer may be from A, B or D but there is only 5% chance. Since C is most likely to be the answer using 1) and 2) separately according to DS definition (It saves us time). Obviously there may be cases where the answer is A, B, D or E.
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Re: In the number 1.4ab5, a and b represent single positive  [#permalink]

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Why not Option (D).

From each option dont we get 10 - X ?

It is already mentioned in both points that if X is .... 10-x is ...
Math Expert V
Joined: 02 Sep 2009
Posts: 56256
Re: In the number 1.4ab5, a and b represent single positive  [#permalink]

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1
somtsat99 wrote:
Why not Option (D).

From each option dont we get 10 - X ?

It is already mentioned in both points that if X is .... 10-x is ...

We need to find the value of 10 - x, so basically the value of x. (1) says that IF x is rounded to the nearest hundredth, then 10 – x = 8.56, which implies that x rounded to the nearest hundredth is 1.44, not x itself. Please re-read the solutions above.
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Re: In the number 1.4ab5, a and b represent single positive  [#permalink]

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1
Top Contributor
shinewine wrote:
In the number 1.4ab5, a and b represent single positive digits. If x = 1.4ab5, what is the value of 10 – x?

(1) If x is rounded to the nearest hundredth, then 10 – x = 8.56.
(2) If x is rounded to the nearest thousandth, then 10 – x = 8.564.

Target question: What is the value of 10 - x?

Given: X = 1.4ab5

Statement 1: If x is rounded to the nearest hundredth, then 10 – x = 8.56
10 - 1.44 = 8.56
So, x rounded to the nearest HUNDREDTH = 1.44
So, x COULD equal 1.4355, 1.4365, 1.4375, 1.4385, 1.4395, 1.4405, 1.4415, 1.4425, 1.4435 OR 1.4445
Given all of the different possible values of x, 10 - x could have MANY different values.
Since we cannot answer the target question with certainty, statement 1 is NOT SUFFICIENT

Statement 2: If x is rounded to the nearest thousandth, then 10 - x = 8.564
10 - 1.436 = 8.564
In other words, x rounded to the nearest THOUSANDTH = 1.436
This tells us that a must equal 3, leaving us with 1.43b5
If 1.43b5 rounded to the nearest THOUSANDTH = 1.436, then b MUST equal 5
So, x must equal 1.4355, which means 10 - x MUST equal 8.5645
Since we can answer the target question with certainty, statement 2 is SUFFICIENT

Cheers,
Brent
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Re: In the number 1.4ab5, a and b represent single positive  [#permalink]

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Statement 1. If x is rounded to nearest hundredth digit, then 10 – x = 8.56 i.e. x = 1.44
This is possible for (a , b) = (3, >5) and (4 , <5). Hence, Insufficient.
Statement 2. If x is rounded to nearest thousandth digit, 10 – x= 8.564 i.e. x = 1.436
This is only possible when a = 3 and b = 5. Hence, Sufficient. Re: In the number 1.4ab5, a and b represent single positive   [#permalink] 21 Dec 2018, 21:43
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