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

Question

Competition Mode Question

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

(2) p = 4, q = 10

GMATinsight · Answer

Question: is p $ q less than 20?

statement 1 : x $ y = 2x^2 - y for all values of x and y

I.e. p $ q = 2p^2 - q

But since we don't know the values of p and q hence

NOT SUFFICIENT

statement 2 : p = 4, q = 10

but since we do NOT know how the operation p $ q gets simplified hence

NOT SUFFICIENT

Combining the two statements

p $ q = 2p^2 - q and p = 4, q = 10

I.e. p $ q = 2*4^2 - 10 = 32-10 = 22 I.e. Greater than 20 hence

SUFFICIENT

Answer:" Option C

freedom128 · Answer

1) p$q = 2p^2 - q
p$q can be either less than 0 or at least 20, depending value of p and q. 
NOT SUFFICIENT

2) p = 4, q = 10
We don't know the meaning of operator $
NOT SUFFICIENT

1)+2)
4$10 = 2*4^2 - 10 =22 > 20
SUFFICIENT

FINAL ANSWER IS (C)

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CrackverbalGMAT · Answer

If we have to answer the question with a definite Yes or No, we need to know how the operator $ is defined along with the values of p and q.
The definition for the function is given in statement I whereas the values of p and q are given in statement II. As such, we may have to combine the statements, but let us quickly analyse Statement I.

From statement I alone, x$y = 2 x^2  – y, for all values of x and y. As per this definition of $, p$q = 2 p^2  – q. So, we are trying to check if 2 p^2  – q < 20.
If p = 4 and q = 10, 2 p^2  – q = 2*16 – 10 = 22. This is not less than 20.
If p = 3 and q = 10, 2 p^2  – q = 2*9 – 10 = 8. This is less than 20.
Statement I alone is insufficient to give us a definite YES or a NO for the question. Answer options A and D can be eliminated. Possible answer options are B, C or E.

Statement II alone is insufficient since we only have the values of p and q but not the definition of the operator. Answer option B can be eliminated.

Combining statements I and II, we have the definition of the operator from statement I and the values of p and q from statement II. This will be sufficient to find a definite YES or NO for the question asked. 
The combination of statements is sufficient. Answer option E can be eliminated.

The correct answer option is C .

Hope that helps!

lacktutor · Answer

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

( Statement1 ): x $ y = 2x^2 - y for all values of x and y
No info about what p and q are.
 Insufficient .

( Statement2 ): p = 4, q = 10
if $ defines +, then 4+10 < 20 (YES)
if $ defines *, then 4*10 > 20 (NO)
 Insufficient

Taken together 1&2, 
 From statement1, we can get a certain operation --> p $ q will be always greater or less than 20 (Always YES or Always NO)
 Sufficient

The answer is C.

exc4libur · Answer

(1) insufic

(2) insufic 
p+q=14<20
p*q=40>20

(1/2) sufic 
f(x$y)=2x^2-y
f(p$q)=2p^2-q=2*16-10=22>20

Ans (C)

Archit3110 · Answer

find p$q<20
#1

x $ y = 2x^2 - y for all values of x and y
value of p&q not know insufficient
#2
p = 4, q = 10
function not know of p$q insufficient
from 1&2
we know ; 2*(4)^2-10 ; 22
IMO C: sufficient

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

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

(2) p = 4, q = 10

unraveled · Answer

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

(1)  x $ y = 2x^2 - y   for all values of x and y
 p $ q = 2 p^2 - q 
Many values greater than or less than 20 are possible.

INSUFFICIENT.

(2) p = 4, q = 10
'$' operation is not defined.

INSUFFICIENT.

Together 1 and 2.
 4 $ 10 = 2 * 4^2 - 10  = 22
22 > 20

SUFFICIENT.

Answer C.

bumpbot · Answer

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

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

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