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

A commercial real estate firm leased office space across two properties, Property X and Property Y. The rental rate per square foot for space in Property X was 20%20\% higher than the rental rate per square foot for space in Property Y. Was the total rental revenue generated from Property X greater than the total rental revenue generated from Property Y?

(1) Property X accounted for more than 45%45\% of the total square feet of office space leased across both properties.
(2) Property Y accounted for less than 54%54\% of the total square feet of office space leased across both properties.

  1. A
    Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
  2. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.Cevap
  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 (2) ALONE is sufficient to answer the question with a definitive 'Yes', but Statement (1) ALONE is not sufficient.
The correct response identifies that Statement (2) alone is sufficient because it establishes that Property X's area share relative to Property Y yields a ratio SXSY>2327\frac{S_X}{S_Y} > \frac{23}{27}. Because 2327>56\frac{23}{27} > \frac{5}{6}, the revenue of Property X is guaranteed to exceed that of Property Y, providing a definitive 'Yes'. Statement (1) alone is insufficient because it permits ratios below 56\frac{5}{6}.

Adım Adım Çözüm

1
Rephrase the question stem in terms of algebraic variables.
Let SXS_X and SYS_Y be the square footage leased in Property X and Property Y, respectively, and let rr be the rate per sq ft for Property Y. The rate for Property X is 1.20r1.20r. Revenue from X is 1.20rSX1.20r S_X and revenue from Y is rSYr S_Y. The question asks whether 1.20rSX>rSY1.20r S_X > r S_Y, which simplifies to asking whether SXSY>11.20=56\frac{S_X}{S_Y} > \frac{1}{1.20} = \frac{5}{6}.
Simplifying the target question into a ratio threshold SXSY>56≈0.8333\frac{S_X}{S_Y} > \frac{5}{6} \approx 0.8333 streamlines the statement evaluation.
2
Evaluate Statement (1): SX>0.45(SX+SY)S_X > 0.45(S_X + S_Y).
0.55SX>0.45SY  ⟹  SXSY>0.450.55=911≈0.81820.55 S_X > 0.45 S_Y \implies \frac{S_X}{S_Y} > \frac{0.45}{0.55} = \frac{9}{11} \approx 0.8182. Since 911<56\frac{9}{11} < \frac{5}{6}, SXSY\frac{S_X}{S_Y} could be 0.820.82 (giving a 'No' answer to the question) or 1.01.0 (giving a 'Yes' answer).
Statement (1) allows values both above and below the required threshold of 5/65/6, making it insufficient.
3
Evaluate Statement (2): SY<0.54(SX+SY)S_Y < 0.54(S_X + S_Y).
0.46SY<0.54SX  ⟹  SXSY>0.460.54=2327≈0.85190.46 S_Y < 0.54 S_X \implies \frac{S_X}{S_Y} > \frac{0.46}{0.54} = \frac{23}{27} \approx 0.8519. Comparing 2327\frac{23}{27} and 56\frac{5}{6}: 23×6=13823 \times 6 = 138 and 27×5=13527 \times 5 = 135. Since 138>135138 > 135, 2327>56\frac{23}{27} > \frac{5}{6}. Thus, SXSY\frac{S_X}{S_Y} must be strictly greater than 56\frac{5}{6}.
Statement (2) forces SXSY\frac{S_X}{S_Y} to be strictly greater than 5/65/6, yielding a definitive 'Yes' to the question stem.

Anahtar Kavram

Question Stem Rephrasing and Threshold Analysis in Data Sufficiency Ratio Problems
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Rates, Ratios, Percentages, and Applied Word Problems

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