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

Question

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.

Bunuel · Accepted Answer

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. Answer: B. 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 https://gmatclub.com/forum/download/file.php?id=20515 Hope it helps. Place Values.png

gmatcrook · Answer

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.

shinewine · Answer

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..

Futuristic · Answer

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

shinewine · Answer

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.

fozzzy · Answer

What's the OA for this question?

somtsat99 · Answer

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 ...

Bunuel · Answer

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.

BrentGMATPrepNow · Answer

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

Given : X = 1.4 ab 5

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 1.4 35 5, 1.4 36 5, 1.4 37 5, 1.4 38 5, 1.4 39 5, 1.4 40 5, 1.4 41 5, 1.4 42 5, 1.4 43 5 OR 1.4 44 5
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 1.4 3b 5
If 1.4 3b 5 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

masoomjnegi · Answer

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.

TestPrepUnlimited · Answer

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

GMATGuruNY · Answer

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.

B

Kimberly77 · Answer

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

BrentGMATPrepNow · Answer

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

Kimberly77 · Answer

Thanks Brent

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

Apeksha2101 · Answer

Great explaination

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

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