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BSchool Forum Moderator V
Joined: 29 Jan 2015
Posts: 1466
Location: India
WE: General Management (Non-Profit and Government)
Rounded to the nearest unit, x=?  [#permalink]

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Difficulty:   75% (hard)

Question Stats: 33% (01:27) correct 67% (01:22) wrong based on 39 sessions

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Rounded to the nearest unit, x=?

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

(2) Rounded to the nearest units, x/3=1
Intern  B
Joined: 17 May 2018
Posts: 48
Re: Rounded to the nearest unit, x=?  [#permalink]

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2
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.

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Manager  B
Joined: 27 Jun 2015
Posts: 56
GRE 1: Q158 V143 Re: Rounded to the nearest unit, x=?  [#permalink]

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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.

Intern  B
Joined: 17 May 2018
Posts: 48
Rounded to the nearest unit, x=?  [#permalink]

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vishumangal wrote:
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.

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?
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Current Student B
Affiliations: All Day Test Prep
Joined: 08 May 2018
Posts: 75
Location: United States (IL)
Schools: Booth '20 (A)
GMAT 1: 770 Q51 V49 GRE 1: Q167 V167 GPA: 3.58
Re: Rounded to the nearest unit, x=? (1) Rounded to the nearest unit, 6x=9  [#permalink]

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MBA20 wrote:
Rounded to the nearest unit, x=?
(1) Rounded to the nearest unit, 6x=9
(2) Rounded to the nearest units, x/3=1

A. Statement (1) ALONE is sufficient but Statement (2) ALONE is not sufficient.
B. Statement (2) ALONE is sufficient but Statement (1) ALONE is not sufficient.
C. BOTH Statements TOGETHER are sufficient, but NEITHER Statement alone is sufficient.
D. Each Statement ALONE is sufficient.
E. Statements (1) and (2) TOGETHER are NOT sufficient.

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

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Unlimited private GMAT Tutoring in Chicago for less than the cost a generic prep course. No tracking hours. No watching the clock. Re: Rounded to the nearest unit, x=? (1) Rounded to the nearest unit, 6x=9   [#permalink] 02 Apr 2019, 11:36
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