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Re: To qualify for an interview for a computer-programming job [#permalink]
1
Lester wrote:
To qualify for an interview for a computer-programming job, each candidate must be able to program in at least one of three specified computer languages. Of the 15 candidates who qualify for an interview, 3 can program in all three of the specified languages and 4 can program in only one of the specified languages

Quantity A
Quantity B
The number of candidates who qualify for an interview and who can program in at least two of the specified languages
9


A) Quantity A is greater.
B) Quantity B is greater.
C) The two quantities are equal.
D) The relationship cannot be determined from the information given.


Every candidate can program in at least one language, we can write:
(number of candidates who can program in exactly 1 language) + (number of candidates who can program in exactly 2 languages) + (number of candidates who can program in all languages) = 15

Substitute to get:
4 + (number of candidates who can program in exactly 2 languages) + 3 = 15
So, number of candidates who can program in exactly 2 languages = 8

The number of candidates who can program in at least two of the specified languages = (number of candidates who can program in exactly 2 languages) + (number of candidates who can program in all languages)
= 8 + 3
= 11

Answer: A
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Re: To qualify for an interview for a computer-programming job [#permalink]
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Let's break down the information given:

Total number of candidates who qualify for an interview: 15
Number of candidates who can program in all three specified languages: 3
Number of candidates who can program in only one specified language: 4
To find the number of candidates who can program in at least two of the specified languages, we need to consider those who can program in all three languages and those who can program in two languages (excluding those who can only program in one language).

So, the number of candidates who can program in at least two languages = (Candidates who can program in all three languages) + (Candidates who can program in two languages)

= 3 (candidates who can program in all three languages) + (Total candidates who qualify for an interview - candidates who can program in only one language)

= 3 + (15 - 4)
= 3 + 11
= 14

So, Quantity A (14) is greater than Quantity B (9).

Therefore, the correct answer is option A) Quantity A is greater.
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