BTGModeratorVI wrote: ↑Tue Mar 31, 2020 5:05 am
If y^c = y^(d+1), what is the value of y?
(1) y < 1
(2) d = c
Answer:
C
Source: Princeton Review
A few considerations:
case 1) If y = 1, then y^c = y^(d+1) for ALL values of c and d
case 2) If y = 0, then y^c = y^(d+1) for ALL values of c and d
case 3) If y = -1, then y^c = y^(d+1) if c and (d+1) are both ODD or both EVEN
case 4) If y equals any value OTHER THAN 1, 0 or -1, then y^c = y^(d+1) only if c and (d+1) are EQUAL
Target question: What is the value of y?
Given: y^c = y^(d+1)
Statement 1: y < 1
This rules out
case 1 above.
However, this still leaves several possibilities that yield conflicting answers to the target question.
Here are two:
Case a: y = 0, c = 1 and d = 1. Notice that this satisfies the given information [y^c = y^(d+1)] because 0^1 = 0^(1+1). In this case
y = 0
Case b: y = 3, c = 2 and d = 1. Notice that this satisfies the given information [y^c = y^(d+1)] because 3^2 = 3^(1+1). In this case
y = 3
Since we cannot answer the
target question with certainty, statement 1 is NOT SUFFICIENT
Statement 2: d = c
This rules out
cases 3 and 4 above. Here's why:
case 3: if c and d are equal, then c and (d+1) CANNOT both be EVEN or ODD
case 4: if c and d are equal, then c and d+1 cannot be equal
However, this still leaves several possibilities that yield conflicting answers to the target question.
Here are two:
Case a: y = 0, c = 1 and d = 1. Notice that this satisfies the given information [y^c = y^(d+1)] because 0^1 = 0^(1+1). In this case
y = 0
Case b: y = 1, c = 1 and d = 1. Notice that this satisfies the given information [y^c = y^(d+1)] because 1^1 = 1^(1+1). In this case
y = 1
Since we cannot answer the
target question with certainty, statement 2 is NOT SUFFICIENT
Statements 1 and 2 combined
Statement 1 rules out
case 1 above
Statement 2 rules out
cases 3 and 4 above
This leaves only
case 2, which means
y must equal 0
Since we can answer the
target question with certainty, the combined statements are SUFFICIENT
Answer: C
Cheers,
Brent
