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If z denotes the tenths digit in the decimal representation of the tim 26 May 2020, 02:27
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95% (hard)

Question Stats:

37% (02:07) correct 63% (02:40) wrong based on 194 sessions

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T = 2.z hours
If z denotes the tenths digit in the decimal representation of the time T that a car takes to cover 258 miles, what is the value of z?

(1) The speed of the car is 1 mile per minute, rounded to the nearest integer
(2) When T is rounded to the nearest 100 minutes, the result is 200.

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If z denotes the tenths digit in the decimal representation of the tim 26 May 2020, 03:47
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Bunuel
T = 2.z hours
If z denotes the tenths digit in the decimal representation of the time T that a car takes to cover 258 miles, what is the value of z?

(1) The speed of the car is 1 mile per minute, rounded to the nearest integer
(2) When T is rounded to the nearest 100 minutes, the result is 200.

Show more

Solution


Step 1: Analyse Question Stem


    • T = 2.z hours
    • z denotes the tenths digit in the decimal representation of the time T taken to cover a distance of 258 miles.
    • We need to find the value of z.

Step 2: Analyse Statements Independently (And eliminate options) – AD/BCE


Statement 1: The speed of the car is 1 mile per minute, rounded to the nearest integer
    • Let the speed of the car be s miles per hour.
      o Then, \(0.5*60 ≤ s < 1.5*60 ⟹ 30≤ s < 90\)
    • Since distance is constant, so higher the speed lesser will be the time taken to cover 258 miles.
      o Therefore, time taken to travel a distance of 258 miles is: \(\frac{258}{90} < T ≤ \frac{258}{30}\)
         Thus, \(2.86 < T ≤ 8.6 ⟹ 2.86 < 2.z < 2.95\)
         If we round off the numbers from 2.86 to 2.95, excluding both, to their nearest tenth digit, the result will always be 2.9.
          • Thus, z = 9
Hence, statement 1 is sufficient and we can eliminate answer Options B, C and E.

Statement 2: When T is rounded to the nearest 100 minutes, the result is 200
    • \(2.z\) hours \(= 2*60 + 0.z*60 = 120 + 6z\) minutes
    • According to this statement, \(150 ≤ 120 + 6z < 250\)
      \(⟹ 30 ≤ 6z < 130 \)
      \(⟹ 5 < z < 21. 67\)
    • Since, z is a single digit so, z can be 6, 7, 8, or 9.
    • Here we cannot determine the unique value of z.
Hence, statement 2 is NOT sufficient.
Thus, the correct answer is Option A.
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If z denotes the tenths digit in the decimal representation of the tim 26 May 2020, 12:46
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GMATWhizTeam



Thus, \(2.86 < T ≤ 8.6 ⟹ 2.86 < 2.z < 2.95\)
 If we round off the numbers from 2.86 to 2.95, excluding both, to their nearest tenth digit, the result will always be 2.9.
Show more

Hi GMATWhizTeam,

How did 8.6 become 2.95? while the LHS (2.86) remained the same? Can you please explain that part!

Thank you
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If z denotes the tenths digit in the decimal representation of the tim 26 May 2020, 19:33
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abcdddddd
GMATWhizTeam



Thus, \(2.86 < T ≤ 8.6 ⟹ 2.86 < 2.z < 2.95\)
 If we round off the numbers from 2.86 to 2.95, excluding both, to their nearest tenth digit, the result will always be 2.9.

Hi GMATWhizTeam,

How did 8.6 become 2.95? while the LHS (2.86) remained the same? Can you please explain that part!

Thank you
Show more

Hi,

We already know T=2.z hours. This means T will always be less than 3. So the range becomes 2.86 to 2.99.
We have obtained the range in the form of 2.zx, but we need it to be in the form of 2.z. For this, we need to round it to 1 decimal point while maintaining the units place as 2.
Therefore, the range becomes \(2.86 < T ≤ 8.6 ⟹ 2.86 < 2.z < 2.95\)
Any value > 2.95 will round it up to 3.

Thanks
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Thus, \(2.86 < T ≤ 8.6 ⟹ 2.86 < 2.z < 2.95\)
 If we round off the numbers from 2.86 to 2.95, excluding both, to their nearest tenth digit, the result will always be 2.9.

Hi GMATWhizTeam,

How did 8.6 become 2.95? while the LHS (2.86) remained the same? Can you please explain that part!

Thank you
Show more

Heyabcdddddd

We only need to focus on the time which when rounded off to its tenth digit will be in the form of 2.z. So, according to the statement 1 even though we are getting time's range as \(2.86 < T ≤ 8.6 \), we are decreasing its upper limit to 2.95 i.e.\(2.86 < T < 2.95 \).
Now the question comes why are we decreasing it to less than 2.95 only? This is because if \(2.95 ≤ T ≤ 8.6\) and it is rounded off to it's tenth digit, the time won't be in the form of 2.z or the unit's digit of T won't be 2.
For example, if T = 2.95 then it's hundredth's digit is ≥ 5. So when it is rounded up to its tenth's digit the result will be 3.0

Hope that helps! :)

Regards,
GMATwhiz Team
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If z denotes the tenths digit in the decimal representation of the tim 15 Sep 2022, 12:29
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