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kingflo
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21 Jul 2013, 10:54
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C
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If the positive integer x is rounded to the nearest ten, will the result be greater than x ?
(1) If x is divided by 10, the remainder is even.
(2) If x is divided by 5, the remainder is odd.
(1) If x is divided by 10, the remainder is even.
(2) If x is divided by 5, the remainder is odd.
21 Jul 2013, 11:08
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If the positive integer x is rounded to the nearest ten, will the result be greater than x ?
(1) If x is divided by 10, the remainder is even --> the units digit of x is even: 0, 2, 4, 6, or 8.
If the units digit of x is 0, 2, or 4, then x rounded to the nearest ten will be less than x (for example, if x=2, then x rounded to the nearest ten will be 0<2).
If the units digit of x is 6, or 8, then x rounded to the nearest ten will be greater than x (for example, if x=16, then x rounded to the nearest ten will be 20>16).
Not sufficient.
(2) If x is divided by 5, the remainder is odd --> the units digit of x is 1, 3, 6 or 8.
If the units digit of x is 1 or 3, then x rounded to the nearest ten will be less than x (for example, if x=11, then x rounded to the nearest ten will be 10<11).
If the units digit of x is 6, or 8, then x rounded to the nearest ten will be greater than x (for example, if x=28, then x rounded to the nearest ten will be 30>28).
Not sufficient.
(1)+(2) From above it follows that the units digit of x is either 6 or 8. In any case x rounded to the nearest ten will be greater than x. Sufficient.
Answer: C.
Hope it's clear.
(1) If x is divided by 10, the remainder is even --> the units digit of x is even: 0, 2, 4, 6, or 8.
If the units digit of x is 0, 2, or 4, then x rounded to the nearest ten will be less than x (for example, if x=2, then x rounded to the nearest ten will be 0<2).
If the units digit of x is 6, or 8, then x rounded to the nearest ten will be greater than x (for example, if x=16, then x rounded to the nearest ten will be 20>16).
Not sufficient.
(2) If x is divided by 5, the remainder is odd --> the units digit of x is 1, 3, 6 or 8.
If the units digit of x is 1 or 3, then x rounded to the nearest ten will be less than x (for example, if x=11, then x rounded to the nearest ten will be 10<11).
If the units digit of x is 6, or 8, then x rounded to the nearest ten will be greater than x (for example, if x=28, then x rounded to the nearest ten will be 30>28).
Not sufficient.
(1)+(2) From above it follows that the units digit of x is either 6 or 8. In any case x rounded to the nearest ten will be greater than x. Sufficient.
Answer: C.
Hope it's clear.
General Discussion
stonecold
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30 Aug 2016, 12:40
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Here is my approach for this one =>
Here firstly the word "ten" must be replaced by tens. I know its an integer but still its good to label them up correctly.
Now we are asked if x rounded to tens would be greater than x or not.
For that to happen the unit digit must be greater than 4 i.e 5,6,7,8,9
Its a YES/NO question .
Lets look at the statements =>
Statement 1 => the unit digit can be 0,2,4,6,8 .
Remember that digit constraint allows only 10 values for any digit .
Hence here if the unit digit is 0,2,4 => No
This is because if the unit digit is zero then the two values would be equal and if they are 2 or 4 then the rounded number would result in a smaller number.
If the unit digit of x=6 or 8 => the rounded number will always be greater than the original number.
Hence this statement is clearly insufficient.
Lets look at statement 2 =>
Here the unit digit of x can be 1,3,6,8
Hmm Again if the unit digit is 1 or 3 => The rounded number would be lesser than the original number.=>Answer=NO
But if the unit digit is 6 or 8 => The rounded number would always be greater than the original number.Answer=YES
Hence this statement is insuff too
Now combining them
we can say that unit digit of x must either be a 6 or an 8 => the rounded number would always be greater than the original number => Answer = YES
Hence this statement is suff to answer out question
SMASH THAT C
Here firstly the word "ten" must be replaced by tens. I know its an integer but still its good to label them up correctly.
Now we are asked if x rounded to tens would be greater than x or not.
For that to happen the unit digit must be greater than 4 i.e 5,6,7,8,9
Its a YES/NO question .
Lets look at the statements =>
Statement 1 => the unit digit can be 0,2,4,6,8 .
Remember that digit constraint allows only 10 values for any digit .
Hence here if the unit digit is 0,2,4 => No
This is because if the unit digit is zero then the two values would be equal and if they are 2 or 4 then the rounded number would result in a smaller number.
If the unit digit of x=6 or 8 => the rounded number will always be greater than the original number.
Hence this statement is clearly insufficient.
Lets look at statement 2 =>
Here the unit digit of x can be 1,3,6,8
Hmm Again if the unit digit is 1 or 3 => The rounded number would be lesser than the original number.=>Answer=NO
But if the unit digit is 6 or 8 => The rounded number would always be greater than the original number.Answer=YES
Hence this statement is insuff too
Now combining them
we can say that unit digit of x must either be a 6 or an 8 => the rounded number would always be greater than the original number => Answer = YES
Hence this statement is suff to answer out question
SMASH THAT C
