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Range for Rounding OFF ?

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by andy123 » Mon Mar 14, 2011 1:54 am
The numbers x and y are not integers. the value of x is closest to which integer?

(1) 4 is the integer that is closest to x+y
(2) 1 is the integer that is closest to x-y


Please read the question below:

Not sure if I should take it as --

statement 1 means that 3.4 < x + y < 4.5

OR

3.5 < x+y < 4.5

--


AND:

statement 2 as:

0.4 < x - y < 1.5

OR

0.5 < x-y < 1.5

Please help.
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by Geva@EconomistGMAT » Mon Mar 14, 2011 2:18 am
andy123 wrote:The numbers x and y are not integers. the value of x is closest to which integer?

(1) 4 is the integer that is closest to x+y
(2) 1 is the integer that is closest to x-y


Please read the question below:

Not sure if I should take it as --



statement 1 means that 3.4 < x + y < 4.5

3.5 is the mid point between 3 and 4. Anything smaller than 3.5 is closer to 3 than it is to 4, so this version is wrong: should be 3.5 < x+y < 4.5
OR

3.5 < x+y < 4.5

--


AND:

statement 2 as:

0.4 < x - y < 1.5
Same here: between 0.4 and 0.5 , there are still values of the difference: this inequality allows x-y to equal 0.45, or 0.47, or 0.49999 - all of which are closer to zero than to 1. therefore, this inequality is a wrong mathematical modeliing of the statement: should be the one below.
OR

0.5 < x-y < 1.5

Please help.
Geva
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by andy123 » Mon Mar 14, 2011 2:20 am
Ohh Thanks a lot.

I was thinking of rounding :(
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by Geva@EconomistGMAT » Mon Mar 14, 2011 2:27 am
andy123 wrote:Ohh Thanks a lot.

I was thinking of rounding :(
This is the same logic as rounding: when rounding to the nearest unit (as this question does), go to the units digit and look at the next one (the tenths): if that digit is 0-4, round down. If that digit is 5-9, round up.

Thus, when rounding 3.4, or 3.45, or 3.49999 to the nearest unit, we would round down to 3, as the next digit after the units digit is 4 in all of these cases.
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by krusta80 » Mon Mar 14, 2011 4:02 am
Shouldn't your lower bounds inequalities by less than or equal to rather than strictly less than??
Geva@MasterGMAT wrote:
andy123 wrote:The numbers x and y are not integers. the value of x is closest to which integer?

(1) 4 is the integer that is closest to x+y
(2) 1 is the integer that is closest to x-y


Please read the question below:

Not sure if I should take it as --



statement 1 means that 3.4 < x + y < 4.5

3.5 is the mid point between 3 and 4. Anything smaller than 3.5 is closer to 3 than it is to 4, so this version is wrong: should be 3.5 < x+y < 4.5
OR

3.5 < x+y < 4.5

--


AND:

statement 2 as:

0.4 < x - y < 1.5
Same here: between 0.4 and 0.5 , there are still values of the difference: this inequality allows x-y to equal 0.45, or 0.47, or 0.49999 - all of which are closer to zero than to 1. therefore, this inequality is a wrong mathematical modeliing of the statement: should be the one below.
OR

0.5 < x-y < 1.5

Please help.
Top
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by Geva@EconomistGMAT » Mon Mar 14, 2011 4:08 am
krusta80 wrote:Shouldn't your lower bounds inequalities by less than or equal to rather than strictly less than??

when rounding, strictly speaking, yes. But this question says that the sum of difference are physically closer to one of the integers (4 and 1), so they need to be over the midway point.
Geva@MasterGMAT wrote:
andy123 wrote:The numbers x and y are not integers. the value of x is closest to which integer?

(1) 4 is the integer that is closest to x+y
(2) 1 is the integer that is closest to x-y


Please read the question below:

Not sure if I should take it as --



statement 1 means that 3.4 < x + y < 4.5

3.5 is the mid point between 3 and 4. Anything smaller than 3.5 is closer to 3 than it is to 4, so this version is wrong: should be 3.5 < x+y < 4.5
OR

3.5 < x+y < 4.5

--


AND:

statement 2 as:

0.4 < x - y < 1.5
Same here: between 0.4 and 0.5 , there are still values of the difference: this inequality allows x-y to equal 0.45, or 0.47, or 0.49999 - all of which are closer to zero than to 1. therefore, this inequality is a wrong mathematical modeliing of the statement: should be the one below.
OR

0.5 < x-y < 1.5

Please help.
Last edited by Geva@EconomistGMAT on Mon Mar 14, 2011 4:55 am, edited 1 time in total.
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by fskilnik@GMATH » Mon Mar 14, 2011 4:47 am
Many people believe that 2.5 should be rounded to 3 (if we have to choose between 2 and 3, for sure) by some "misterious convention", but the fact is that this is exactly the same as to believe that a cup that is exactly half-full (and exactly half-empty, of course) should be "only" referred as (say) "half-full"...

The fact is that 2.5 is equally distant from 2 and 3, therefore all meaningful roundings (to be chosen between 2 and 3) are related to STRICLY less than 2.5 (choose 2) and STRICTLY greater than 2.5 (choose 3), simple as that.

The previous paragraph understood, when it is said that "4 is the integer that is closest to x+y" , that means mathematically that 3.5 < x+y < 4.5, and that´s EXACTLY what Geva wrote.

Regards,
Fabio.
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