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by swapna » Mon Feb 01, 2010 11:30 am

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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.


Answer:
To determine the value of 10-x, we must determine the exact value of x. To determine the value of x, we must find out what digits a and b represent. Thus, the question can be rephrased: What is a and what is b?

(1) INSUFFICIENT: This tells us that x rounded to the nearest hundredth must be 1.44. This means that a, the hundredths digit, might be either 3 (if the hundredths digit was rounded up to 4) or 4 (if the hundredths digit was rounded down to 4). This statement alone is NOT sufficient since it does not give us a definitive value for a and tells us nothing about b.

(2) SUFFICIENT: This tells us that x rounded to the nearest thousandth must be 1.436. This means, that a, the hundredths digit, is equal to 3. As for b, the thousandths digit, we know that it is followed by a 5 (the ten-thousandths digit); therefore, if x is rounded to the nearest thousandth, b must rounded UP. Since b is rounded UP to 6, then we know that b must be equal to 5. Statement (2) alone is sufficient because it provides us with definitive values for both a and b.

The correct answer is B.

Can some one explain...how rounding a digit works???i guess i am nt clear on that and hence confusion wid ths explanation
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by sars72 » Mon Feb 01, 2010 11:49 am

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rounding a digit centres on the value 5. If the digit is mre than or equal to 5, then the preceding digit is increased by 1. If the digit is less than 5, then the preceeding digit is left as-is.

e.g. 156 rounded off to the nearest tens = 160, because 6 > 5
and 1.672 rounded to the nearest hundredth = 1.67 coz 2< 5

now, back to our question

10-1.4abb5=?
1) if x rounded ff to nearest hundredth, then 10-x = 8.56
--> 10-1.4a = 8.56 or 10-1.4a= 8.55
this doesn't tell us the value of a or b --> Eliminated
2) If x is rounded to the nearest thousandth, then 10-x = 8.564.
--> 10-1.4ab = 8.564
for the thousandth digit, since 4 can be obtained by 10-6, but b cannot be 6 since if it was 6, the ten thousandth digit of value 'b' would have come into play. Thus, b must be 5 , since on roudning off, it would have increased the thousandth digit by 1 to 6. a is 9-6 = 3

Thus, we will be able to answer 10-1.4abb5 using statement 2

Therefore the answer is B
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by ajith » Mon Feb 01, 2010 11:55 am

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swapna 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.


Answer:
To determine the value of 10-x, we must determine the exact value of x. To determine the value of x, we must find out what digits a and b represent. Thus, the question can be rephrased: What is a and what is b?

(1) INSUFFICIENT: This tells us that x rounded to the nearest hundredth must be 1.44. This means that a, the hundredths digit, might be either 3 (if the hundredths digit was rounded up to 4) or 4 (if the hundredths digit was rounded down to 4). This statement alone is NOT sufficient since it does not give us a definitive value for a and tells us nothing about b.

(2) SUFFICIENT: This tells us that x rounded to the nearest thousandth must be 1.436. This means, that a, the hundredths digit, is equal to 3. As for b, the thousandths digit, we know that it is followed by a 5 (the ten-thousandths digit); therefore, if x is rounded to the nearest thousandth, b must rounded UP. Since b is rounded UP to 6, then we know that b must be equal to 5. Statement (2) alone is sufficient because it provides us with definitive values for both a and b.

The correct answer is B.

Can some one explain...how rounding a digit works???i guess i am nt clear on that and hence confusion wid ths explanation
Rules for rounding decimals.
1.) Identify the number in the position you are rounding to.
Then look at the number to the right of that number.
2) a. If the number to the right is 5 or greater, increase the
number in the rounding position by 1 (round up).
b. If the number to the right is less than 5, leave the
number in the rounding position alone (round down).
3)

a. If you are rounding to a decimal place, drop all
numbers to the right of the number in the rounding
position.
b. If you are rounding to a whole number, replace all
numbers between the rounding position and the
decimal place with zeroes, and drop all decimal places.



.
Always borrow money from a pessimist, he doesn't expect to be paid back.
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by thephoenix » Mon Feb 01, 2010 11:57 am

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s1) 10-x=8.56--->x=1.44 original x=1.4ab5
now when x is rounded to 100th dig resultant x sud be 1.44
if x=1.4435;here a=4 and b=3
x rounded upto 100th dig will be 1.44
and if x=1.4425;whereas now a=4 and b=2 , x rounded upto 100th dig will be 1.44

hence 2 possibilities
insuff

s2)10-x=8.564--->x=1.436
now when x=1.4ab5 is rounded upto 1000th digit resultant x shud be 1.436
3when x=1.4355 is rounded to 1000th dig x=1.436 and here a= and b=5

when x=1.4356 is rounded to 1000th dig x=1.436 and here a= 3and b=5

when x=1.4357 is rounded to 1000th dig x=1.436 and here a= 3and b=5

when x=1.4358 is rounded to 1000th dig x=1.436 and here a= 3and b=5

when x=1.4359 is rounded to 1000th dig x=1.436 and here a= 3and b=5
hence a and b have same value and therefore suff
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Re: help required

by Brent@GMATPrepNow » Wed Jan 15, 2020 2:58 pm

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swapna wrote: ↑
Mon Feb 01, 2010 11:30 am
 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

Answer: B

Cheers,
Brent
Brent Hanneson - Creator of GMATPrepNow.com
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