A bakery sells only vanilla cupcakes and chocolate cupcakes. On Monday, what was the ratio… — GMAT

A bakery sells only vanilla cupcakes and chocolate cupcakes. On Monday, what was the ratio of the number of vanilla cupcakes sold to the number of chocolate cupcakes sold?

(1) On Monday, the bakery sold a total of 120 cupcakes.
(2) On Monday, 40% of the cupcakes sold were vanilla cupcakes.

A
Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.Cevap
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.

Cevap

Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.

The correct answer states that Statement (2) alone is sufficient while Statement (1) alone is not. Statement (1) gives only the sum of both types of cupcakes, which allows for infinite possible ratio combinations. Statement (2) specifies that vanilla cupcakes represent 40% of the total sales, meaning chocolate cupcakes represent the remaining 60%. The ratio of vanilla to chocolate cupcakes is therefore fixed at 40:60, or 2:3, providing a unique and definitive solution.

Adım Adım Çözüm

Rephrase the question stem target algebraically

Let

V

be the number of vanilla cupcakes sold and

C

be the number of chocolate cupcakes sold. The goal is to find the value of the ratio

\frac{V}{C}

Simplifying the target helps determine what information is necessary to answer the question.

Evaluate Statement (1) independently

Statement (1) gives

V + C = 120

. With no information about

V

C

individually, the ratio

\frac{V}{C}

could be

1:1

(60 of each),

1:2

(40 vanilla, 80 chocolate), or many other values. Thus, Statement (1) is NOT sufficient.

A total count alone cannot determine a ratio without additional proportional constraints.

Evaluate Statement (2) independently

Statement (2) states

V = 0.40(V + C)

. Expanding gives

V = 0.40V + 0.40C \implies 0.60V = 0.40C \implies \frac{V}{C} = \frac{0.40}{0.60} = \frac{2}{3}

. A single, unique ratio of

2:3

is determined. Thus, Statement (2) IS sufficient.

Knowing the percentage component of a two-part total fixes the ratio regardless of total volume.

Anahtar Kavram

Determining ratios from component percentages versus absolute quantities in Data Sufficiency

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