You have to decide whether the data given in the statements is sufficient to…
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You have to decide whether the data given in the statements is sufficient to answer the question or draw the conclusion of the statement in the question.
Is X greater than Y?
A. X2+5X+6=0.
B. Y2+16Y+63=0.
- A.
if statement A alone is sufficient but B alone is not sufficient
- B.
if statement B alone is sufficient but statement A alone is not sufficient
- C.
if both statements A and B are needed
- D.
if either of statement A or statement B alone is sufficient.
Attempted by 277 students.
Show answer & explanation
Correct answer: C
Conclusion: X > Y when both statements are used together.
First statement (given equation for X): X^2 + 5X + 6 = 0 factors as (X + 3)(X + 2) = 0, so X = -3 or X = -2.
Second statement (given equation for Y): Y^2 + 16Y + 63 = 0 factors as (Y + 9)(Y + 7) = 0, so Y = -9 or Y = -7.
Using only the first statement you cannot determine X > Y because Y is unknown; using only the second statement you cannot determine X > Y because X is unknown. Thus each statement alone is insufficient.
Combining both statements gives possible X values {−3, −2} and possible Y values {−9, −7}. Every X-value is greater than every Y-value, so in all cases X > Y.
Therefore, both statements together are sufficient to conclude that X > Y, while each statement alone is not.