gmatophobia wrote:
PS Question 1 - June 19 A can complete a project in 20 days and B can complete the same project in 30 days. If A and B start working on the project together and A quits 10 days before the project is completed, in how many days will the project be completed? (A) 18 days (B) 27 days (C) 26.67 days (D) 16 days (E) 12 days Source: GMAT Paper Tests | Difficulty: Hard
They work for a total of t days
Person A will therefore contribute 1/20(d-10)
and person B will therefore contribute (1/30)(d)
which means:
1/20(d-10)+1/30(d)=1
d/20-1/2+d/30=1
d/20+d/30=3/2
3d+2d=90
5d=90
d=18
A
mysterymanrog wrote:
They work for a total of t days Person A will therefore contribute 1/20(d-10) and person B will therefore contribute (1/30)(d) which means: 1/20(d-10)+1/30(d)=1 d/20-1/2+d/30=1 d/20+d/30=3/2 3d+2d=90 5d=90 d=18 A
d days, not t days
gmatophobia wrote:
DS Question 1 - June 19 Is |1 - 4k| > k? (1) k > 4x^3 (2) k < 2x – x^2 - 2 Source: GMATPrepNow | Difficulty: Hard
Great Question!
First thing to notice is that the above inequality will always hold if k is some negative value (since abs has minimum value of 0, which is always greater than any negative number).
You can solve the equation to get more specific ranges:
k<1/5 or k>1/3
1)
Suppose x=2
then we have k>4*8>1/3 (always yes)
Suppose x=-2
k>-32 (maybe yes, maybe no - if k<1/5, yes if 1/5<k<1/3, no)
ins
2) k<-x^2+2x-2
This is a tricky quadratic to factorize. So lets plugin some values:
if x=0,
k<-2, always true
if x=1,
k<-1+2-2
k<-1, target statement always true
if x=2
k<-4+4-2
k<-2 (always true).
if x=-2
k<-4+2(-2)-2
In any case, k is some negative value - which means the target equation must always hold true, as the abs(anything) is 0 or greater.
B should be correct
mysterymanrog wrote:
Great Question! First thing to notice is that the above inequality will always hold if k is some negative value (since abs has minimum value of 0, which is always greater than any negative number). You can solve the equation to get more specific ranges: k<1/5 or k>1/3 1) Suppose x=2 then we have k>4*8>1/3 (always yes) Suppose x=-2 k>-32 (maybe yes, maybe no - if k<1/5, yes if 1/5<k<1/3, no) ins 2) k<-x^2+2x-2 This is a tricky quadratic to factorize. So lets plugin some values: if x=0, k<-2, always true if x=1, k<-1+2-2 k<-1, target statement always true if x=2 k<-4+4-2 k<-2 (always true). if x=-2 k<-4+2(-2)-2 In any case, k is some negative value - which means the target equation must always hold true, as the abs(anything) is 0 or greater. B should be correct
2nd statement is probably best analyzed graphically - but that might be overkill for most gmat questions haha