In City X, it snowed on 68 percent of the days. However, 80 percent of

Question

In City X, it snowed on 68 percent of the days. However, 80 percent of the days when it was not supposed to snow, it snowed and 40 percent of the days when it was supposed to snow, it did not snow. Of the days when it did not snow, what percent of the days it was supposed to snow?

(A) 22%
(B) 32%
(C) 60%
(D) 75%
(E) 80%

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ravi1522 · Accepted Answer

Hello ,
Lets take suppose to snow as Y and not supposed to snow as X and total as 100 for calculation

Snow  
 No snow  
 total 
 
  Supposed to Snow  
 0.6Y  
 0.4Y  
 Y  
 
  Not Supposed to Snow  
 0.8X  
 0.2X  
 X  
 
  Total  
 68  
 32

SO we need 0.4Y*100/32
As per table we will get 2 equation

.6Y+0.8X=68

0.4Y+0.2X=32

when we solve for y we get Y =60

Hence 0.4*60*100/32=75%
Option D is correct

I hope it helps and if you like it please give me kudos

Thanks

GMATinsight · Answer

Let's solve this step by step using a grid.

- Let the total number of days be  100  for simplicity.
 - Given: 
 - It was supposed to snow on 68 days.
 - It was not supposed to snow on 32 days.
 - 40% of the days when it was supposed to snow, it did not snow.
 - 80% of the days when it was not supposed to snow, it snowed.

Step 2: Construct a Probability Grid 
    Weather Condition  
  Supposed to Snow  
  Not Supposed to Snow  
  Total  
 
   Snowed  
  68 × 0.6 = 40.8  
  32 × 0.8 = 25.6   
  66.4  
 
   Did Not Snow  
  68 × 0.4 = 27.2   
  32 × 0.2 = 6.4   
  33.6  
 
   Total  
  68  
  32  
  100

(27.2 / 33.6) × 100 = 80%

Answer:  Option E

ManifestDreamMBA · Answer

Exp S 
 Exp NS 
 Total 
 
  Act S 
 = 1-n -0.4+0.4n = 0.6(1-n) 
 0.8n 
 0.68 
 
  Act NS 
 0.4(1-n) 
 =1-0.8n = 0.2n 
 =1-0.68 = 0.32 
 
  Total 
 1-n 
 n 
 1

0.6(1-n) + 0.8n = 0.68
0.6 - 0.6n + 0.8n = 0.68
0.2n = 0.08
20n = 8
n = .4

Of the days when it did not snow, what percent of the days it was supposed to snow?
= 0.4(1-0.4)/0.32
=4*6/32
= 75%

pranjal1105 · Answer

It snowed on 68 days, and did not snow on 32 days. The grid is wrong.

ajay0520 · Answer

lets consider total no of days supposed to snow and not snow be (N+S) =100
which means, actual snowed days =68
which means actual no snow = 32

now we have actual snow day = 80% of days not suppose to snow(N) + 60% of days expected to snow(S)

which means 68=0.8*N+0.6*S
 or 68= 0.8*(100-s)+0.6S
 this implies s=60( no of days expected to snow)

which means D is correct answer

varunkeeja · Answer

lets make a matrix for this first-
supposed to snow (ss), not supposed to snow (nss), snow (s), did not snow (ns).
 SS NSS. T
 S. 0.6X. 0.8Y 68
 NS 0.4X. 0.2Y. 32
 T. X. Y. 100
we will make equations-
1 0.6x + 0.8Y = 68= 3x+4y=340
2 0.4x + 0.2y= 32= 2x + y= 160

solve for x we get, x=60
so, ans will be 0.4*60= 24 = 24/32= 75%

In City X, it snowed on 68 percent of the days. However, 80 percent of

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	Snow	No snow	total
Supposed to Snow	0.6Y	0.4Y	Y
Not Supposed to Snow	0.8X	0.2X	X
Total	68	32

Weather Condition	Supposed to Snow	Not Supposed to Snow	Total
Snowed	68 × 0.6 = 40.8	32 × 0.8 = 25.6	66.4
Did Not Snow	68 × 0.4 = 27.2	32 × 0.2 = 6.4	33.6
Total	68	32	100

	Exp S	Exp NS	Total
Act S	= 1-n -0.4+0.4n = 0.6(1-n)	0.8n	0.68
Act NS	0.4(1-n)	=1-0.8n = 0.2n	=1-0.68 = 0.32
Total	1-n	n	1

GMAT Problem Solving (PS) Questions

In City X, it snowed on 68 percent of the days. However, 80 percent of

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