If t denotes the thousandths digit in the decimal representation of d

SOLUTION

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.

For more check Number Theory chapter of Math Book: math-number-theory-88376.html

BACK TO THE ORIGINAL QUESTION:

d = 0.43t7
If t denotes the thousandths digit in the decimal representation of d above, what digit is t?

(1) If d were rounded to the nearest hundredth, the result would be 0.44. Just says that \(t\geq{5}\). Not sufficient.

(2) If d were rounded to the nearest thousandth, the result would be 0.436. Since 7 is more than 5, then \(t\) was rounded up to become 6, hence \(t=5\). Sufficient.

Answer: B.

Kudos points given to everyone with correct solution. Let me know if I missed someone.

Not sure if B is correct.

In GMAT can we assume that rounding means rounding up if >=0.5 and rounding down if <0.5? Could also be always rounding up or down (no matter what digit)

This is a question from Official Guide and the Official Answer is B. Rounding rules are given in the second post: if-t-denotes-the-thousandths-digit-in-the-decimal-138297.html#p1119527

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.

If t = 4 -> d = 0.4347 = 0.435 = 0.44
=> t >= 4 not t >= 5

Am I right?

No.

When rounding to the tenth you look at only the hundredth digit, when rounding to the hundredth you look at only the thousandth digit, etc. Please re-read rounding rules given above.

Hi avgroh,

St-I talks about rounding off to the nearest hundredth. Since the number is 0.43t7 and 3 is at the hundredths place, for rounding off to the nearest hundredth we will only consider the value of the digit next to it. As 0.43t7 has been rounded off to 0.44 that would mean t =>5.

Rounding off from the right most digit is not the right way to go about rounding off process. Think of it this way: Consider the number 1.448 which is to be rounded off to the nearest tenths. If you start from the right most digit you would round off it as 1.448 -> 1.45 -> 1.5.
But 1.448 is nearer to 1.4 than to 1.5, right? Hence the only thing that should matter is the next digit to which a number is to be rounded off. Hence for the number 1.448, to round it off to the nearest tenths, the digit next to tenths place i.e. 4 should matter and it should be rounded off to 1.4.

Hope it's clear

Regards
Harsh

We are given that t denotes the thousandths digit of 0.43t7. We need to determine the value of t.

Statement One Alone:

If d were rounded to the nearest hundredth, the result would be 0.44.

Using the information in statement one, t could be different values. For example, t could be 5 (so that d would be 0.4357) or t could be 6 (so that d would be 0.4367). Similarly, t could also be 7, 8, or 9. Notice in any of these cases, d rounds up to 0.44.

Thus, statement one is not enough information to answer the question. We can eliminate answer choices A and D.

Statement Two Alone:

If d were rounded to the nearest thousandth, the result would be 0.436.

Using the information from statement two, d must be 0.4357. Because of the “7” in the ten-thousandths digit, we see that 0.43t7 will only round up to 0.436. Thus, t can only be the value 5. Any other value of t will not round d to 0.436 when rounded to the nearest thousandth. Statement two is sufficient to answer the question.

The answer is B.

Hi Bunuel
Should not it be more than 4 (5¬9)?
Thanks__

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