In the number 1.4ab5, a and b represent single positive

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..
https://academic.brooklyn.cuny.edu/geolo ... ndoff.html
Please corect me..

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

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.

What's the OA for this question?

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.

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.

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:

Cheers,
Brent

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.

it does not work....

i tried over this question after going through your free video lecture and marked my right logically solved ques to wrong :P.

Analyzing the question:
We must figure out both a and b to answer this.

Statement 1:
This gives \(x = 1.44\) after rounding, then \(1.435 <= x < 1.445\) before rounding. This can confirm a = 3 or a = 4 depending on the value of b but still insufficient.

Statement 2:
We repeat the same process, \(x = 1.436\) after rounding. Then we can say \(1.4355 <= x < 1.4365\), and a = 3 with b = 5 or 6. However, notice our last digit is confirmed to be 5. We cannot choose 1.4365 as that would force us to round up to 1.437. Then x must be 1.4355 and that is sufficient.

Answer: B

We round UP when we reach HALFWAY between two values.
Any value BELOW the halfway point is rounded DOWN.



Statement 1, with x isolated:
If x is rounded to the nearest hundredth, then x=1.44.
Plotting 1.44 between 1.43 and 1.45, we get:
1.43.....1.435.....1.44.....1.445.....1.45
The range in blue is rounded to 1.44:
1.435 ≤ x < 1.445
Since x must have a ten-thousands digits of 5, different options are possible.
Here are two:
x = 1.4355
x = 1.4365
Since x can be different values, INSUFFICIENT.

Statement 2:
If x is rounded to the nearest thousandth, then x=1.436.
Plotting 1.436 between 1.435 and 1.437, we get:
1.435.....1.4355.....1.436.....1.4365.....1.437
The range in blue is rounded to 1.436:
1.4355 ≤ x < 1.4365
Since x must have a ten-thousands digits of 5, only one option is possible:
x = 1.4355
SUFFICIENT.

Hi BrentGMATPrepNow, In Statement 1, x rounded to the nearest HUNDREDTH = 1.44. Why is a =4 here and not any other values e.g 1.45 or 1.41.....etc? Same with statement 2 for b please?
Also is given values of 8.56 & 8.564 any relevant here? Thanks Brent

Statement 1: If x is rounded to the nearest hundredth, then 10 – x = 8.56
When we solve this equation for x, we get x = 1.44
This means, that when x, rounded to the nearest hundredth, equals 1.44

Thanks Brent . What a silly mistake. Think time for a break now.

Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.