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Zorluk: KolayRates, Ratios, Percentages, and Applied Word Problems

A boutique fitness studio offers only yoga and pilates classes. What is the ratio of the number of yoga classes to the number of pilates classes offered each week?

(1) Yoga classes account for 60% of the total number of classes offered each week.
(2) The total number of classes offered each week is 40.

  1. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.Cevap
  2. B
    Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.
  3. C
    BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
  4. D
    EACH statement ALONE is sufficient.
  5. E
    Statements (1) and (2) TOGETHER are NOT sufficient.

Cevap

Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
The correct answer identifies that Statement (1) alone is sufficient because knowing that yoga classes account for 60% of total classes implies pilates classes account for 40%, giving a fixed ratio of 60 to 40 (or 3 to 2). Statement (2) only provides the total number of classes without any relative distribution, making it insufficient on its own.

Adım Adım Çözüm

1
Rephrase the target question
We need to find the ratio Y:PY : P, where YY is the number of yoga classes and PP is the number of pilates classes. Note that total classes T=Y+PT = Y + P.
Simplifying the target helps determine whether percentage data or numerical data is needed.
2
Evaluate Statement (1)
If yoga classes are 60% of the total TT, then Y=0.60TY = 0.60T. Since the studio offers only yoga and pilates classes, pilates classes account for the remaining 40%, so P=0.40TP = 0.40T. The ratio Y:P=0.60T0.40T=6040=32Y : P = \frac{0.60T}{0.40T} = \frac{60}{40} = \frac{3}{2}.
Statement (1) yields a unique numerical ratio of 3:23:2. Thus, Statement (1) alone is SUFFICIENT.
3
Evaluate Statement (2)
Statement (2) gives T=40T = 40. We have Y+P=40Y + P = 40, but without knowing the proportion or count of either class type, Y:PY : P can take multiple values (e.g., 20:20=1:120:20 = 1:1 or 30:10=3:130:10 = 3:1).
Statement (2) alone does not give a unique ratio. Thus, Statement (2) alone is INSUFFICIENT.

Anahtar Kavram

Data Sufficiency with Ratios and Percentages
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Rates, Ratios, Percentages, and Applied Word Problems

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