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# If t denotes the thousandths digit in the decimal

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If t denotes the thousandths digit in the decimal [#permalink]  03 Sep 2012, 05:04
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81% (01:51) correct 19% (00:52) wrong based on 372 sessions
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.
(2) If d were rounded to the nearest thousandth, the result would be 0.436.

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Re: If t denotes the thousandths digit in the decimal [#permalink]  03 Sep 2012, 05:04
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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.

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Re: If t denotes the thousandths digit in the decimal [#permalink]  03 Sep 2012, 05:27
1
KUDOS
Statement (1): d is rounded up. So the thousandth digit can take the values 5, 6, 7, 8, 9. --> not sufficient
Statement (2): d is again rounded up, because the tenthousandths digit is 7. Therefore, the thousands digit is 5. --> sufficient

Answer B, Statement (2) is sufficient, Statement (1) is not sufficient.
Math Expert
Joined: 02 Sep 2009
Posts: 27184
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Kudos [?]: 40974 [0], given: 5616

Re: If t denotes the thousandths digit in the decimal [#permalink]  07 Sep 2012, 04:29
Expert's post
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.

Kudos points given to everyone with correct solution. Let me know if I missed someone.
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Re: If t denotes the thousandths digit in the decimal [#permalink]  23 Oct 2014, 05:11
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Re: If t denotes the thousandths digit in the decimal [#permalink]  26 Dec 2014, 08:22
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)
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Re: If t denotes the thousandths digit in the decimal [#permalink]  26 Dec 2014, 08:25
Expert's post
noshtafoyza wrote:
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.
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Re: If t denotes the thousandths digit in the decimal   [#permalink] 26 Dec 2014, 08:25
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