Multiple choice

Directions: The following problem consists of a question and three statements numbered I, II and III given below it. You have to decide which of the given statements is/are sufficient to answer the question. Read all the statements and give answer accordingly. How many girls went to see the live cricket match in the stadium? I. The ratio of the number of boys to that of girls who watched the match was 7 : 5. II. If there were 12 more boys, the ratio of the number of the boys to that of girls who watched the match would be 3 : 2. III. The total strength of the stadium is 288. (The total number of boys and girls who went to watch the match was 288.)

  1. I and II only

  2. II and III only

  3. III only

  4. Any of the two statement is sufficient.

  5. None of these
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Statement I gives the ratio of boys to girls. Statement III gives the total number of people. With I and III, we can solve for the number of girls. Statement II provides a hypothetical scenario that also allows solving for the initial number of girls when combined with I. Thus, either (I and III) or (I and II) is sufficient.

AI explanation

Using statements one and two, we can solve for the number of girls by setting up the proportion 7x divided by 5x plus 12 equals 3 divided by 2, which gives 14x equals 15x plus 36, making the number of girls 180. Statements one and three provide the total strength of 288 and the boy to girl ratio of 7 to 5, meaning the 12 parts equal 288, so the 5 parts representing girls equal 120. Statements two and three provide the total of 288 and the modified ratio of 3 to 2, allowing you to form the equation for the new total of 300 and solve for the girls. Therefore, any two of the three statements are sufficient to find the number of girls.

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