$x is enough for Bob to survive 45 days, while for Amy $x is enough to

Question

$x is enough for Bob to survive 45 days, while for Amy $x is enough to survive only for 36 days. How many days they can survive together for total of $2x ?

A. 10 days
B. 20 days
C. 30 days
D. 40 days
E. 50 days

M37-77

Bunuel · Accepted Answer

Official Solution:

$x  is enough for Bob to survive exactly 45 days, while for Amy  $x  is enough to survive only exactly 36 days. How many days they can survive together for total of  $2x  ?

A.  10  days
B.  20  days
C.  30  days
D.  40  days
E.  50  days

For one day Bob needs  $\frac{x}{45}  and Amy needs  $\frac{x}{36} . Together, for one day they'd need  $\frac{x}{45} + $\frac{x}{36}=$\frac{x}{20} .
 
On  $2x  they'll survive for  \frac{2x}{\frac{x}{20}}=40  days.

Answer: D

GMATWhizTeam · Answer

Solution 
We can also solve it as time and work problem
 • Let’s assume x as the LCM(45, 36)
 o x = 180 units 
• The amount required by Bob to survive one day =  \frac{180}{45} = 4  units
• The amount required by Amy to survive one day =  \frac{180}{36} = 5  units
 o The amount required by both of them together to survive one day =  4 + 5 = 9  units
o In 180 units they can survive =  \frac{180}{9} = 20 days
o With $  x  they can survive =  20  days
o With $ 2x  they can survive = 2*20=40  days  
Hence, the correct answer is  Option D.

Alternative method: 
 • The amount required by Bob to survive 45 days = x
 o The amount required by Bob to survive 1 day =  \frac{x}{45}  
• The amount required by Amy to survive 36 days = x
 o The amount required by Amy to survive 1 day =  \frac{x}{36}  
• Amount required by both of them to survive 1 day =  \frac{x}{45} + \frac{x}{ 36} = \frac{(5x + 4x)}{180} = \frac{x}{20} 
 o With  \frac{x}{20}  they both can survive 1 day
o With  x , they can survive for 20days
o With $  2x  they can survive for 40 days 
 
Thus, the correct answer is  Option D.

fireagablast · Answer

x = r1*45 -->r1=x/45
x = r2*36 --> r2=x/36

2x = (x/45+x/36)t
2x = (4x/180+5x/180)t
2x = (9x/180)t
2x = (x/20)t
40=t

100na · Answer

Bob =1/45,amy=1/36
Together 1/45+1/36=20days
$xdays=20days
$2xdays=2×20=40days

Posted from my mobile device

CrackverbalGMAT · Answer

This is essentially a Time & Work question; do not let it fool you because it talks about money being spent.  The money with which Bob/Amy can survive represents the work to be done .
 
As with most Time & Work problems, the LCM method works very well in this case. We can assume x to be the LCM of 45 and 36.
x = LCM (45,36) = $180

If Bob can survive 45 days with $180, it means he uses up $4 per day. Similarly, Amy uses up $5 per day.  These values represent the individual rates of Bob and Amy .
If they have to survive together, they will consume a total of $9 per day. If a total of $360 is available, they can survive for a total of 40 days ( \frac{360}{9} ).

The correct answer option is D .

Hope that helps!

Anurocks1233 · Answer

Bunuel  Can we not use AM in this case ? 45+36 /2 = 40.5 hence D

$x is enough for Bob to survive 45 days, while for Amy $x is enough to

Prep Toolkit

Top 5 GMAT Debrief Videos

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards

GMAT Problem Solving (PS) Questions

$x is enough for Bob to survive 45 days, while for Amy $x is enough to

Prep Toolkit

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards