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# Is it true that x rounded to the nearest tenth is equal to y rounded

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Math Expert
Joined: 02 Sep 2009
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Is it true that x rounded to the nearest tenth is equal to y rounded  [#permalink]

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04 Sep 2016, 05:49
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65% (hard)

Question Stats:

56% (01:41) correct 44% (01:54) wrong based on 163 sessions

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Is it true that x rounded to the nearest tenth is equal to y rounded to the nearest tenth?

(1) (10x) rounded to the nearest unit is equal to (10y) rounded to the nearest unit.

(2) (x/10) rounded to the nearest hundredth is equal to (y/10) rounded to the nearest hundredth.

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Re: Is it true that x rounded to the nearest tenth is equal to y rounded  [#permalink]

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04 Sep 2016, 05:57
1
It should be D.
The 1st (as well as the 2nd) statements alone implies that x rounded to the nearest tenth is equal to y rounded to the nearest tenth.
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Re: Is it true that x rounded to the nearest tenth is equal to y rounded  [#permalink]

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04 Sep 2016, 07:48
it Must be E

without knowing the value of X and Y it isn't possible to determine the answer.
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Re: Is it true that x rounded to the nearest tenth is equal to y rounded  [#permalink]

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04 Sep 2016, 10:45

1.Multiplying by 10 shifts the decimal toright.Since 10x=10y .The tenth digit becomes unit

2.Dividing by 10 shifts decimal to left.Tenth digit becomes hundreth.
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Re: Is it true that x rounded to the nearest tenth is equal to y rounded  [#permalink]

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15 Dec 2016, 12:30
AARTHIK wrote:
it Must be E

without knowing the value of X and Y it isn't possible to determine the answer.

Yea for example if X=.512 and Y=.542 then 10X=5.12 and 10Y=5.42. Both rounded to the nearest unit is 5. Therefore their tenths digit place rounded to the nearest tenth do not equal each other (.51 and .54). Same goes for the second statement. You could also pick numbers that make the question true such as .512 and .513.
That is why I picked E.
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Re: Is it true that x rounded to the nearest tenth is equal to y rounded  [#permalink]

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16 Dec 2016, 07:08
ryuken101 wrote:
AARTHIK wrote:
it Must be E

without knowing the value of X and Y it isn't possible to determine the answer.

Yea for example if X=.512 and Y=.542 then 10X=5.12 and 10Y=5.42. Both rounded to the nearest unit is 5. Therefore their tenths digit place rounded to the nearest tenth do not equal each other (.51 and .54). Same goes for the second statement. You could also pick numbers that make the question true such as .512 and .513.
That is why I picked E.

The question asked if both x and y rounded to the tenth are equal to each other. In the example you gave of .512 and .542, both rounded to tenth are still equal at .5 . Same for statement 2. IMO D.
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Is it true that x rounded to the nearest tenth is equal to y rounded  [#permalink]

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09 Jan 2018, 23:11
ryuken101 wrote:
AARTHIK wrote:
it Must be E

without knowing the value of X and Y it isn't possible to determine the answer.

Yea for example if X=.512 and Y=.542 then 10X=5.12 and 10Y=5.42. Both rounded to the nearest unit is 5. Therefore their tenths digit place rounded to the nearest tenth do not equal each other (.51 and .54). Same goes for the second statement. You could also pick numbers that make the question true such as .512 and .513.
That is why I picked E.

I almost forget math knowledge.
The problem wants to ask about the number with decimal, I thought both X and Y are integers.
Lesson here: rounded to the nearest number -> decimal numbers.
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Is it true that x rounded to the nearest tenth is equal to y rounded  [#permalink]

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11 Jan 2018, 08:53
Bunuel wrote:
Is it true that x rounded to the nearest tenth is equal to y rounded to the nearest tenth?

(1) (10x) rounded to the nearest unit is equal to (10y) rounded to the nearest unit.

(2) (x/10) rounded to the nearest hundredth is equal to (y/10) rounded to the nearest hundredth.

Forget conventional ways of solving math questions. For DS problems, the VA (Variable Approach) method is the quickest and easiest way to find the answer without actually solving the problem. Remember that equal numbers of variables and independent equations ensure a solution.

The first step of the VA (Variable Approach) method is to modify the original condition and the question, and then recheck the question.

Let's analyze how to get the nearest tenth. The nearest tenth of 1.345 is 1.3 and that of 1.456 is 1.5.
Thus we define the nearest tenth as follows.

If n - 1/2 ≤ 10x < n + 1/2 where n is an integer, n/10 is the nearest tenth.

10 * 1.345 = 13.45
13 - 1/2 = 12.5 ≤ 13.45 < 13.5 = 13 + 1/2
13/10 = 1.4 is the nearest tenth of 1.345.

10 * 1.456 = 14.56
15 - 0.5 = 14.5 ≤ 14.56 < 15.5 = 15 + 0.5
15/10 = 1.5 is the nearest tenth of 1.456.

Condition 1):

The definition of the nearest unit of 10x is as follows.
If n - 0.5 ≤ 10x < n + 0.5, n is the nearest unit of 10x and n/10 is the nearest tenth of x.

Thus condition 1) is same as the definition of nearest tenth of x.
The condition 1) is sufficient.

Condition 2):

If n - 0.5 ≤ 100 * (x/10) < n + 0.5, n/100 is the nearest hundredth of (x/10), which is equivalent to the definition of the nearest tenth that n/10 is the nearest tenth of x.

Thus condition 2) is same as the definition of nearest tenth of x.
The condition 2) is sufficient.

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Re: Is it true that x rounded to the nearest tenth is equal to y rounded  [#permalink]

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18 Jul 2019, 19:50
2
Bunuel wrote:
Is it true that x rounded to the nearest tenth is equal to y rounded to the nearest tenth?

(1) (10x) rounded to the nearest unit is equal to (10y) rounded to the nearest unit.

(2) (x/10) rounded to the nearest hundredth is equal to (y/10) rounded to the nearest hundredth.

Let x=ab.cd and y = ab.ce, where a,b,c,d,e are digits
To find: whether x=y after rounding to the tenth digit. This is only possible when the digits d and e are both below 5 or greater than equal to 5.

(1) 10x = abc.d and 10y=abc.e after rounding are only equal when both d and e are either both below 5 or both greater than equal to 5. Sufficient.

(2) x/10 = a.bcd and y/10=a.bce after rounding to hundredth digits are only equal when both d and e are either both below 5 or both greater than equal to 5. Sufficient.

D is correct.
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Re: Is it true that x rounded to the nearest tenth is equal to y rounded  [#permalink]

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19 Jul 2019, 02:16
kapil1 wrote:
Bunuel wrote:
Is it true that x rounded to the nearest tenth is equal to y rounded to the nearest tenth?

(1) (10x) rounded to the nearest unit is equal to (10y) rounded to the nearest unit.

(2) (x/10) rounded to the nearest hundredth is equal to (y/10) rounded to the nearest hundredth.

Let x=ab.cd and y = ab.ce, where a,b,c,d,e are digits
To find: whether x=y after rounding to the tenth digit. This is only possible when the digits d and e are both below 5 or greater than equal to 5.

(1) 10x = abc.d and 10y=abc.e after rounding are only equal when both d and e are either both below 5 or both greater than equal to 5. Sufficient.

(2) x/10 = a.bcd and y/10=a.bce after rounding to hundredth digits are only equal when both d and e are either both below 5 or both greater than equal to 5. Sufficient.

D is correct.

This is the best method for this type of questions. Thanks a lot!!!
Re: Is it true that x rounded to the nearest tenth is equal to y rounded   [#permalink] 19 Jul 2019, 02:16
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