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D
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Difficulty:
85%
(hard)
Question Stats:
35% (01:32) correct
65%
(01:10)
wrong
based on 91
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If x=y, is it true that x rounded to the nearest tenths is equal to the exact value of y?
(1) y is equal to x rounded to the tenths.
(2) y is an integer.
(1) y is equal to x rounded to the tenths.
(2) y is an integer.
24 Aug 2021, 12:32
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Bunuel
Statement 1:
This statement restating the question. Sufficient.
The better statement would be: "y rounded to the nearest tenths is equal to x." Rounding y to the tenths did not change the value of y since we already had x = y before rounding. Then since x = y, rounding x to the tenths will also not change the value of x. Thus no matter who is rounded to the tenths, we will always have x = y.
Statement 2:
Since x and y are both integers, rounding to the tenths will not change their value. Sufficient.
Ans: D
24 Aug 2021, 16:13
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Sometimes I like to use a few examples to "decode" what the questions are really asking......
If X = Y ------> then under what scenario would X rounded to the nearest tenths NOT be equal to the EXACT value of Y?
case 1:
if X = 9.876 ----- then X = Y, so Y = 9.876
when we round X to the nearest tenths: X = 9.9 -----> which is NOT equal to Y = 9.876
case 2:
if X = 9.87 ----- then X = Y, so Y = 9.87
when we round X to the nearest tenths: X = 9.9 -----> which is NOT equal to Y = 9.87
it seems the only way we can have X = Y and then X rounded to the nearest tenths equal to the exact value of Y is when:
the Value of X and Y do NOT have any Digits beyond the tenths decimal place
Question: is X or Y equal to a number that does NOT have a Digit beyond the tenths decimal place?
statement 1: Y is equal to X rounded to the tenths
since Y = X, the exact same digits that make up Y will be the exact same digits that make up X
as shown above, if that number is a number that has digits BEYOND the tenths decimal place, then Statement 1 will never be satisfied, because in such a case, when you round X it will never exactly be equal to Y
X = Y ----> must be of the Form: XXXX . A -- or--- an Integer
just for clarity, taking another example:
Case 1: Given X = Y = 5.23
Y = 5.23
X = 5.23 -----> X rounded to the nearest tenths = 5.2
5.2 does NOT equal 5.23 - and statement 1 is NOT satisfied
Case 2: Given X = Y = 7.9
Y = 7.9
X = 7.9 -----> X rounded to the nearest tenths = 7.9
statement 1 is satisfied as 7.9 = Y = 7.9
and
X rounded to the nearest tenths (7.9) is equal to the exact value of Y (7.9)
S1 is sufficient to answer the Question YES for any case that satisfies statement 1
statement 2: Y is an Integer
since X = Y
then X = that same Integer
rounding any Integer to the tenths decimal place will result in that exact same Integer
Y = X = 6.000 = Integer -----> rounded to the "tenths decimal place: = 6
again, this answers the rephrased Question is X or Y a number that does NOT have a Digit Beyond the tenths decimal place
S2 is Sufficient
D - Each alone are sufficient
If X = Y ------> then under what scenario would X rounded to the nearest tenths NOT be equal to the EXACT value of Y?
case 1:
if X = 9.876 ----- then X = Y, so Y = 9.876
when we round X to the nearest tenths: X = 9.9 -----> which is NOT equal to Y = 9.876
case 2:
if X = 9.87 ----- then X = Y, so Y = 9.87
when we round X to the nearest tenths: X = 9.9 -----> which is NOT equal to Y = 9.87
it seems the only way we can have X = Y and then X rounded to the nearest tenths equal to the exact value of Y is when:
the Value of X and Y do NOT have any Digits beyond the tenths decimal place
Question: is X or Y equal to a number that does NOT have a Digit beyond the tenths decimal place?
statement 1: Y is equal to X rounded to the tenths
since Y = X, the exact same digits that make up Y will be the exact same digits that make up X
as shown above, if that number is a number that has digits BEYOND the tenths decimal place, then Statement 1 will never be satisfied, because in such a case, when you round X it will never exactly be equal to Y
X = Y ----> must be of the Form: XXXX . A -- or--- an Integer
just for clarity, taking another example:
Case 1: Given X = Y = 5.23
Y = 5.23
X = 5.23 -----> X rounded to the nearest tenths = 5.2
5.2 does NOT equal 5.23 - and statement 1 is NOT satisfied
Case 2: Given X = Y = 7.9
Y = 7.9
X = 7.9 -----> X rounded to the nearest tenths = 7.9
statement 1 is satisfied as 7.9 = Y = 7.9
and
X rounded to the nearest tenths (7.9) is equal to the exact value of Y (7.9)
S1 is sufficient to answer the Question YES for any case that satisfies statement 1
statement 2: Y is an Integer
since X = Y
then X = that same Integer
rounding any Integer to the tenths decimal place will result in that exact same Integer
Y = X = 6.000 = Integer -----> rounded to the "tenths decimal place: = 6
again, this answers the rephrased Question is X or Y a number that does NOT have a Digit Beyond the tenths decimal place
S2 is Sufficient
D - Each alone are sufficient
Bunuel
