I29-100

Question

The table shows the performance of 15 professional swimmers who entered a county championship.  Lap time  is the average number of seconds per lap,  stamina score  is a coach-assigned rating out of 100, and  reach  is the arm span of a swimmer, measured from the tip of one middle finger to the tip of the other with both arms fully extended.
      Swimmer   Lap time (sec)   Stamina score   Reach (inches)       Allen   34.1   82   74       Barton   32.8   78   79       Chen   31.0   69   72       Diaz   36.4   92   81       Evans   33.5   88   70       Foster   37.2   74   82       Grant   35.6   71   77       Hughes   30.9   85   73       Ibrahim   33.8   80   78       Jensen   32.1   95   76       Kim   34.9   67   83       Lopez   31.3   90   71       Mason   36.7   79   80       Nash   35.2   72   75       Olsen   30.5   98   84      
For each statement, select  Yes  if it is true based on the table. Otherwise, select  No.

Bunuel · Answer

Official Solution:

• The median stamina score is greater than the median reach. 
 
With 15 swimmers, the median is the 8th largest value. The stamina scores in order give a median of 80 (8th value). The reaches in order give a median of 77 (8th value). Since 80 > 77, the statement is true.
 
Answer:  Yes 
 
 • Stamina score is directly proportional to reach. 
 
If two values are directly proportional, each stamina score divided by reach would give the same ratio. This is not the case here. For example, Diaz has 92/81 ≈ 1.14, while Kim has 67/83 ≈ 0.81. Because the ratios differ, stamina score is not directly proportional to reach.
 
Answer:  No 
 
 • If one swimmer is selected at random, the probability that the swimmer’s lap time is below 32.3 seconds or the reach is above 75 inches is 12/15. 
 
Lap time below 32.3: 4 swimmers (Olsen, Hughes, Chen, Lopez).
 Reach above 75: 9 swimmers (Jensen, Grant, Ibrahim, Barton, Mason, Diaz, Foster, Kim, Olsen).
 
However, one swimmer, Olsen, belongs to both lists. So the total count is 4 + 9 − 1 = 12. Probability = 12/15. The statement is true.
 
Answer:  Yes

Correct answer:

The median stamina score is greater than the median reach.  "Yes"

Stamina score is directly proportional to reach.  "No"

If one swimmer is selected at random, the probability that the swimmer’s lap time is below 32 seconds or the reach is above 75 inches is 12/15.  "Yes"

toan999 · Answer

I did not quite understand the solution. the first sentence is weird. Why do we compare 2 measures with different units? (score and inches)

Bunuel · Answer

The statement itself is asking you to compare the median stamina score to the median reach, even though they have different units. In this question, “greater than” is just a numerical comparison of the median values, not a claim that the two quantities are directly comparable in a physical sense.

So you are not interpreting 80 points as “longer” than 77 inches. You are only checking whether the number that happens to be the median stamina score is larger than the number that happens to be the median reach. The units do not matter for the truth of that specific statement, because the statement is purely about the numeric values shown in the table.

I29-100

Prep Toolkit

Top 5 GMAT Debrief Videos

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards

Swimmer	Lap time (sec)	Stamina score	Reach (inches)
Allen	34.1	82	74
Barton	32.8	78	79
Chen	31.0	69	72
Diaz	36.4	92	81
Evans	33.5	88	70
Foster	37.2	74	82
Grant	35.6	71	77
Hughes	30.9	85	73
Ibrahim	33.8	80	78
Jensen	32.1	95	76
Kim	34.9	67	83
Lopez	31.3	90	71
Mason	36.7	79	80
Nash	35.2	72	75
Olsen	30.5	98	84