Decimals

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Decimals

by abhirup1711 » Fri Jun 07, 2013 4:35 am
In the number 10.6pq5, p and q represents digits. If z = 10.6pq5, what is the value of 12 - z?
1.when z is rounded to nearest thousanth, 12 - z = 1.324
2. when z is rounded to the nearest hundredth, 12 - z = 1.32

Please help

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by fcabanski » Fri Jun 07, 2013 12:45 pm
Someone can reply with the answer to this question. Does GMAT use standard rounding (next digit 0,1,2,3,4 keep the number, next digit 5,6,7,8,9 add one to the number), or does GMAT use banker's rounding? Banker's rounding changes if the next digit is 5. If it's 5 and nothing follows it (or only 0's) then if the preceding number is even keep it, but if the preceding number is odd round up to the even number.

.145 Standard rounded to nearest hundredth is .15, but banker's rounded to nearest hundredth is .14.

The following answer assumes standard rounding.

Anticipate needed info: the statement must somehow deliver a definite value for p and q. If either p or q can be more than one value, then the statement isn't sufficient.

12.0000 - 10.6pq5 = x. That means 12 - x = 10.6pq5

1. When z is rounded to nearest thousanth, 12 - z = 1.324. 12 - 1.324 = z (rounded) = 10.676. Since the last digit of z is 5, the third (thousandths) digit rounded up from 5 to 6. That means z was originally 10.6755. 12-10.6755 = 1.3245. Sufficient. Eliminate B, C, and E. A and D are possible answers.

2. When z is rounded to the nearest hundredth, 12 - z = 1.32. That means z (rounded to nearest hundredth) is 12-1.32 = 10.68. The next number, q, could be anything. It could be 0,1,2,3,4 which made q=8 (it stayed the same when rounded.) q could be 5,6,7,8,9 which made p=7 (it went up when rounded). 2. doesn't provide a definitive value for p or q. It isn't sufficient. Eliminate D.

A is the answer.
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by srcc25anu » Fri Jun 07, 2013 1:39 pm
St1: z can be anything from 10.6755 to 10.6764 bacause it must give 10.676 on being rounded to nearest thousandth.
But we know the last digit is 5 so only choice is 10.6755.
Sufficient

St2: z can be anything from 10.675 to 10.684 because it must give 10.68 on being rounded to nearest hundredth.
It could be 10.6755 or 10.6765 or 10.6775 ....etc
Not Insufficient

Ans A
Last edited by srcc25anu on Fri Jun 07, 2013 2:35 pm, edited 1 time in total.

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by fcabanski » Fri Jun 07, 2013 2:31 pm
"St1: z can be anything from 10.6755 to 10.6764 because it must give 10.676 on being rounded to nearest thousandth. Not Sufficient."

That is not true. The problem specified "z = 10.6pq5". The last digit is a 5. The last digit is not a 4.
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