Four dollar amounts, w, x, y, and z, were invested in a business. Which amount was greatest?
1. y < z < x
2. x was 25 percent of the total of the four investments.
A. Statement 1 alone is sufficient but statement 2 alone is not sufficient to answer the question asked.
B. Statement 2 alone is sufficient but statement 1 alone is not sufficient to answer the question asked.
C. Both statements 1 and 2 together are sufficient to answer the question but neither statement is sufficient alone.
D. Each statement alone is sufficient to answer the question.
E. Statements 1 and 2 are not sufficient to answer the question asked and additional data is needed to answer the statements.
Which should be the correct option and why?
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Statement 1: y < z < xkanika123 wrote:Four dollar amounts, w, x, y, and z, were invested in a business. Which amount was greatest?
1. y < z < x
2. x was 25 percent of the total of the four investments.
No information about w.
INSUFFICIENT.
Statement 2: x was 25 percent of the total of the four investments.
No information about w, y, or z.
INSUFFICIENT.
Statements combined:
Plug in the THRESHOLD.
Since y<z<x, and x=25%, the threshold for y and z is 25%: each must be LESS than this percentage.
If y=z=x=25%, then y+z+x = 75%, implying that w = 25%.
Since y and z must each be LESS than 25%, y+z+x < 75%, implying that w > 25%.
Thus, the greatest amount = w.
SUFFICIENT.
The correct answer is C.
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Hi kanika123,
DS questions test many different skills, one of which is your ability to make deductions when you only have a limited amount of information.
In this question, we're told that there are 4 variables (w, x, y and z) and we're asked which is biggest.
Fact 1 tells us y < z < x BUT we don't know anything about the value of w.
This fact ultimately means that either x is biggest (it's bigger than y and z and MIGHT be bigger than w) or w is biggest
Fact 1 is INSUFFICIENT
Fact 2 tells us that x = 25% of the total We don't know anything about the other 3 values (w, y and z), so there's no way to answer the question.
This fact ultimately means that x can't be biggest (it could be a 4-way tie, if they're each 25%, but if the others were all less than 25% then the math wouldn't add up to 100%, so x can't be biggest).
Fact 2 is INSUFFICIENT
Combining Facts, we know that x = 25%, y and z are both less than 25%, so the w has to account for everything else...
eg. 23% < 24% < 25% and the w would be everything else (in this case = 28%)
We have enough info to deduce that the w MUST be biggest
Final Answer: C
GMAT assassins aren't born, they're made,
Rich
DS questions test many different skills, one of which is your ability to make deductions when you only have a limited amount of information.
In this question, we're told that there are 4 variables (w, x, y and z) and we're asked which is biggest.
Fact 1 tells us y < z < x BUT we don't know anything about the value of w.
This fact ultimately means that either x is biggest (it's bigger than y and z and MIGHT be bigger than w) or w is biggest
Fact 1 is INSUFFICIENT
Fact 2 tells us that x = 25% of the total We don't know anything about the other 3 values (w, y and z), so there's no way to answer the question.
This fact ultimately means that x can't be biggest (it could be a 4-way tie, if they're each 25%, but if the others were all less than 25% then the math wouldn't add up to 100%, so x can't be biggest).
Fact 2 is INSUFFICIENT
Combining Facts, we know that x = 25%, y and z are both less than 25%, so the w has to account for everything else...
eg. 23% < 24% < 25% and the w would be everything else (in this case = 28%)
We have enough info to deduce that the w MUST be biggest
Final Answer: C
GMAT assassins aren't born, they're made,
Rich
