Rounded to the nearest unit, x=?

Question

(1) Rounded to the nearest unit, 6x=9

(2) Rounded to the nearest units, x/3=1

yoannnesme · Answer

Let's start with the second statement, it will be easier to understand.

(2) Rounded to the nearest units, x/3=1. This means that the result of dividing x by 3 is between 0.5 and 1.5 (non inclusive) so that we would round it to one. This translates to:
0.5<x/3<1.5
We multiply everything by 3:
1.5<x<4.5
This statement by itself is not sufficient.

(1) Let's follow the same reasoning for statement 1. We must have:
8.5<6x<9.5
Divide everything by 6, we get approx:
1.4 < x < 1.6
By itself it's not enough, the number can be rounded down or up depending on how close it is to its lower or upper limit.

1) and 2) If we combine the inequalities, we'll have:
1.5<x<1.6
Which means x will be rounded up to 2.

Answer C!

vishumangal · Answer

From the Question stem its is clear that the value of X will be a unit digit

Statement 1--->
X can have multiples values ranging from 1.42 to 1.5
Thus Statement 1 is insufficient

Statement 2-->
X can have values ranging from 1.5 to 3
Thus statement 2 is also insufficient

Combining both the statements will give a Unique value of X = 1.5.

Thus C is the answer

yoannnesme · Answer

I see three inaccuracies in your answer:

1) In Statement 1, x can have multiple values from 1.42 to 1.58
2) In statement 2, x can have values ranging from 1.5 to 4.5
3) If x = 1.5 exactly, you could either round it down or up, so I think it would not be sufficient to answer the question?

alldaytestprep · Answer

1) If 6x rounded to the nearest unit is 9 then 8.5 ≤ 6x < 9.5 - multiply by 10 throughout ---> 85 ≤ 60x < 95 - (85/60) ≤ x < (95/60) -----> Simplified: (17/12) ≤ x < (19/12) - 17/12 will get rounded down to 1, while 19/12 would get rounded up to 2. Therefore, INSUFFICIENT 2) If x/3 rounded to the nearest unit is 1 then .5 ≤ (x/3) < 1.5 - multiply by 3 throughout ---> 1.5 ≤ x < 4.5 - INSUFFICIENT 1 & 2) - separately we know (17/12) ≤ x < (19/12) AND 1.5 ≤ x < 4.5 - therefore together our boundaries are defined by the more limiting extreme - this means 1.5 ≤ x < (17/12) - any value for x within this boundary will be rounded up to 2. Together the statements are SUFFICIENT Answer: C

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Rounded to the nearest unit, x=?

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