How to approach ques such as this?

[anurag_7]

If $ defines a certain operation, is p $ q less than 20?

(1) x $ y = 2x² - y for all values of x and y

(2) p = 4, q = 10

According to me ans should be E but the correct ans is C.

[GMATinsight]

If $ defines a certain operation, is p $ q less than 20?

(1) x $ y = 2x² - y for all values of x and y

(2) p = 4, q = 10

Question : is p $ q less than 20?

[We need to know the meaning op operation $ to answer the question]

Statement 1) x $ y = 2x² - y for all values of x and y

Therefore p $ q = 2p² - q

But since the values of p and q are unknown therefore INSUFFICIENT

Statement 2) p = 4, q = 10
But the meaning of operator $ is unknown therefore INSUFFICIENT

Combining the two statements
[ p $ q = 2p² - q ] and [ p = 4, q = 10 ]

p $ q = 2*4^2 - 10 = 32 - 10 = 22 Which is greater than 20, Answering the question as NO therefore,

SUFFICIENT

Answer: Option C

[Matt@VeritasPrep]

S1 tells us the operation, but not the values of p and q; INSUFFICIENT.

S2 tells us the values of p and q, but not what the operation $ does; INSUFFICIENT.

Together, we know that p $ q = 2p² - q. Since p = 4 and q = 10, we have p $ q = 4 $ 10 = 2*4² - 10 = 22. So we can answer definitively that p $ q is NOT less than 20; SUFFICIENT.

[anurag_7]

Problem solved. Thanks.

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Hi anurag_7,

This DS prompt is a "symbolism" question - a prompt in which a "made-up" symbol is defined, then you're asked to do a simple calculation with it.

The design of this question is interesting though...you DON'T actually have to calculate anything. Fact 1 defines the symbol and Fact 2 tells you what numbers to plug in and where. You COULD calculate the end result and then you would be able to answer the question. Whether the answer is YES or NO is irrelevant because there would be just one answer.

Final Answer: C

Many of the DS questions you'll face on Test Day are built around specific shortcuts and patterns. Spotting these patterns can save you some serious time and "mental strain".

GMAT assassins aren't born, they're made,
Rich