What is the value 120 $ 12 * 6 # 2?
Statement (I): $ means ÷, * means × and # means +.
Statement (II): 16 $ 4 * 2 # 2 = 10
Decide whether the data provided in the statements are sufficient to answer the question.
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → If either I or II is sufficient.
Note: The given answer is as per the official NTA Answer Key. However, there seems to be a mistake in the question: statement (II) alone fits two different meanings of the $ sign, so strictly only statement (I) fixes the value, as explained below. Statement (II) has two ways to make 10, and NTA’s key counted only one of them.
In a question on data sufficiency, a statement is sufficient only if it leads to one fixed value. The expression is worked out in the usual order (BODMAS): × and ÷ from left to right first, then + and −.
Statement (I) alone gives the meaning of every symbol ($ is ÷, * is ×, # is +):
\(120\div12\times6+2=10\times6+2=62\)
So statement (I) alone is sufficient.
Statement (II) alone gives one equation, 16 $ 4 * 2 # 2 = 10, with three unknown symbols. Two sets of meanings fit it:
$ is ÷, * is ×, # is +:
\(16\div4\times2+2=8+2=10\)
the value asked for is then \(120\div12\times6+2=62\)
$ is −, * is ×, # is +:
\(16-4\times2+2=16-8+2=10\)
the value asked for is then \(120-12\times6+2=50\)
Statement (II) therefore allows two values, 62 and 50. NTA’s answer reads statement (II) as pointing to the same meanings as statement (I), which gives 62 from either statement.
Option (1) If I alone is sufficient, while II alone is not sufficient. — Should have been correct. Statement (I) gives 62, while statement (II) also fits $ as a minus, which gives 50.
Option (4) If either I or II is sufficient. — Correct as per NTA; however, it holds only if statement (II) is read as giving $ the meaning ÷, which the equation does not force.