If x is the decimal 8.1d5, with d as an unknown digit, and x

Question

If x is the decimal 8.1d5, with d as an unknown digit, and x rounded to the nearest tenth is equal to 8.1, which digits could not be the value of d?

In order for x to be 8.1 when rounded to the nearest tenth, the right-digit-neighbor, d, must be less than
5. Therefore, d cannot be 5, 6, 7, 8 or 9.

But i feel that d Cannot be 4 as well,bcos 8.145,when rounded off will become 8.15 and then 8.2

Pls correct if my understanding is incorrect

dave785 · Answer

When rounding, you only look at the closest digit to the cutoff point, not any of the ones past it.

Rounding .145 to .2 because you first round the 4 to a 5 would be the same as rounding the number 145 up to 200. 145 is closer to 100 than to 200.. For another example, if we had .4999999 we would never round that number up to 1, because it's closer to 0 than to 1... and that is why we only look at the closest digit.

Zarrolou · Answer

Hi iikarthik,

before posting any question, please check our  rules for posting : you have to provide 5 possible answers.

The solution to your question is (of course) correct

8,1d5  rounded becomes  8,1 : so d can be range from 0 to 4.

X is rounded to the nearest tenth, this means that all the possible values of d (0,1,...,9) will be rounded to the "closest" tenth.

8,145 , in particular is rounded to  8.1 . Distance to  8.1  is  0.045 , distance to  8.2  is  0.055 . Will be rounded to  8.1

Hope this clarifies, let me know

Bunuel · Answer

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. For more check Number Theory chapter of Math Book: math-number-theory-88376.html BACK TO THE ORIGINAL QUESTION: 8.1d5 rounded to the nearest tenth is equal to 8.1 --> the dropped digit is d, thus we are only concerned with it: d cannot be 5, 6, 7, 8, or 9. Hope it helps.

EMPOWERgmatRichC · Answer

Hi All,

If we're rounding the number 8.1d5 to the nearest TENTH and ending up with 8.1, then here's what we know about the digit d:

It COULD be 0, 1, 2, 3, or 4 because these numbers would round DOWN to the nearest tenth, giving us 8.1

It CANNOT be 5, 6, 7, 8, 9 because these numbers would round UP to the nearest tenth, giving us 8.2, which is NOT a match for what we're told.

In this question, it's worth noting that since we're rounding to the nearest TENTH, the "5" in the thousanths place has NO EFFECT on the rounding.

The question asks for which digits COULD NOT be the value of d, so the answer is 5, 6, 7, 8, 9

GMAT assassins aren't born, they're made, 
Rich

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If x is the decimal 8.1d5, with d as an unknown digit, and x

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If x is the decimal 8.1d5, with d as an unknown digit, and x

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