Is y − x

Question

Is y − x < 60 ?

(1) When x and y are rounded to the nearest unit, the results are 15 and 75, respectively.

(2) When x and y are rounded to the nearest ten, the results are 20 and 70, respectively.

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yashikaaggarwal · Answer

To find: Is y − x < 60 ?

(1) When x and y are rounded to the nearest unit, the results are 15 and 75, respectively.

=> Value of X when rounded to nearest unit digit = 15
So value of X can range from 14.51 ≤ X ≤15.49 
=> Value of Y when rounded to nearest unit digit = 75
So value of Y can range from 74.51 ≤ Y ≤75.49

Putting extreme values in Y-X
Case 1: Y = 75.49 & X = 14.51
75.49-14.51 > 60
60.98 > 60 (correct)

Case 2: Y = 74.51 & X = 15.49
74.51-15.49 > 60
59.02 > 60 (Incorrect)
(Insufficient)

(2) When x and y are rounded to the nearest ten, the results are 20 and 70, respectively.

=> Value of X when rounded to nearest ten digit = 20
So value of X can range from 15.01 ≤ X ≤ 24.99
=> Value of Y when rounded to nearest ten digit = 70
So value of Y can range from 65.01 ≤ Y ≤74.99

Putting extreme values in Y-X
Case 1: Y = 74.99 & X = 15.01
74.99-15.01 > 60
59.98 > 60 (incorrect)

Case 2: Y = 65.01 & X = 24.99
65.01-24.99 > 60
40.02 > 60 (Incorrect)
(Sufficient)

Answer is B

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Biswadeep20 · Answer

y and x can be any real number, since they are not mentioned as integers.

Statement 1 states x and y are rounded to the nearest unit, the values are 15 and 75. So we can have 14.7 as the value of x and 75.3 as the value of y. Calculating, we get 60.6, which is definitely more than 60. 
Now, let's take 15.2 and 74.8 as the respective values. Calculating, we get 59.6, which is definitely less than 60. 
Clearly, this statement doesn't always give y-x to be always less than 60. Hence, insufficient.

Statement 2 states x and y when rounded to nearest ten, the values are 20 and 70.
We can take the extreme values quickly. 15 is going to be the farthest possible value and 74.99... is the farthest possible value. Let's consider this value of y to be 75(although it isn't the correct, but we are just assuming a number). Now if we subtract 75 and 15, we get 60. But as we know 75 can never be a number, the maximum value can be 74.999.... So the value also will be less than 60. 
Clearly, this statement is sufficient.

B is the answer!

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TestPrepUnlimited · Answer

Statement 1:

With this we know  14.5 ≤ x < 15.5  and  74.5 ≤ y < 75.5 .

The biggest difference we can get is around 75.5 - 14.5 = 61, so we cannot guarantee y - x is less than 60. Insufficient.

Statement 2:

15 ≤ x < 25  and  65 ≤ y < 75 . The biggest difference is around 75 - 15 = 60. Thus y - x must be less than 60. Sufficient.

Ans: B

stne · Answer

TestPrepUnlimited  Sir,

Minor typo here :
It should be  65 ≤ y < 75 ' Hence biggest difference is around 74-15= 59.

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Is y − x < 60 ? (1) When x and y are rounded to the nearest unit, the

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