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Math Expert V
Joined: 02 Sep 2009
Posts: 58133
If t denotes the thousandths digit in the decimal representation of d  [#permalink]

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17 00:00

Difficulty:   5% (low)

Question Stats: 85% (01:05) correct 15% (01:15) wrong based on 1208 sessions

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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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Math Expert V
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Re: If t denotes the thousandths digit in the decimal representation of d  [#permalink]

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6
13
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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GMAT 1: 770 Q51 V42 Re: If t denotes the thousandths digit in the decimal representation of d  [#permalink]

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1
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 V
Joined: 02 Sep 2009
Posts: 58133
Re: If t denotes the thousandths digit in the decimal representation of d  [#permalink]

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1
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 representation of d  [#permalink]

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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)
Math Expert V
Joined: 02 Sep 2009
Posts: 58133
Re: If t denotes the thousandths digit in the decimal representation of d  [#permalink]

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1
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 representation of d  [#permalink]

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Bunuel wrote:
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.

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

Am I right?
Math Expert V
Joined: 02 Sep 2009
Posts: 58133
Re: If t denotes the thousandths digit in the decimal representation of d  [#permalink]

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avgroh wrote:
Bunuel wrote:
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.

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.
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Re: If t denotes the thousandths digit in the decimal representation of d  [#permalink]

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1
avgroh wrote:
Bunuel wrote:
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.

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

Am I right?

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
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Re: If t denotes the thousandths digit in the decimal representation of d  [#permalink]

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1
Quote:
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.

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.
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