In the number 1.4ab5

[lsadams]

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.

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.


Either I don't understand the question or it's not correclty stated. If we are asked to find out what is 10 - x, both answers choices are giving the answer right away, there is no need to figure out what a and b are.
thanks

[Ben Ku]

Either I don't understand the question or it's not correclty stated. If we are asked to find out what is 10 - x, both answers choices are giving the answer right away, there is no need to figure out what a and b are.

The question asks for the EXACT value of 10-x. The answer choices give us ROUNDED values of 10-x.

[In the following, I use * to indicate that the number is rounded]
(1) Here, 10 - 1.4a* = 8.56, so 1.4a* is 1.44*. a could be 3 if b >=5, or a could be 4 if b < 5. Insufficient.
(2) Here, 10 - 1.4ab* = 8.564 so 1.4ab* is 1.436*. Here, we know for sure a = 3. We also know b = 5, because 1.4355 rounded to the nearest hundredth is 1.436. If we know both a and b, then we know x, and we can find out exactly 1-x. Sufficient.

[avinashsbajaj]

Hi,

Looking at this question type, I had a doubt:

When I look at certain GMAT problems that require rounding-off of the numbers, I notice a slight discrepancy:

In GMAT problems, when 0.225 is rounded-off to the nearest hundredth, will it be 0.23 or 0.22??

I ask this because in one particular problem in OG10, I noticed that the rounding-off was similar to the latter, hence disturbing my conventional thinking.

Answer to this question will answer my query.

Thanks in advance.

[Ben Ku]

0.225, when rounded to the hundredth, should be 0.23. I'm not sure which OG problem would have it rounded otherwise.