Each of the 110 residents in Dashville is either a rancher or

Question

Each of the 110 residents in Dashville is either a rancher or a tractor-driver, but not both. How many residents of Dashville are ranchers?

(1) There are more than 81 ranchers who reside in Dashville

(2) The number of ranchers who reside in Dashville is less than three times the number of tractor-drivers who reside in Dashville

stne · Answer

(1) There are more than 81 ranchers who reside in Dashville :
 So Ranchers + TD = 110
 82+28=110
 83+27=110
 84+26=110 
 .... ......Etc INSUFF.

(2) The number of ranchers who reside in Dashville is less than three times the number of tractor-drivers who reside in Dashville:
 Ranchers + TD = 110
 82+28 =110
 81+29=110 
 80 +30=110
 79+31=110
 ...........etc 
 INSUFF.

1+2 
 81+29 =110 Not allowed according to statement one 
 82+28 =110  Only this case is possible  
 83+27 =110 Not allowed according to statement two
SUFF.

Ans-C

donu · Answer

How isn't statement 83+27 = 110 not allowed by statement 2?

Bunuel · Answer

Each of the 110 residents in Dashville is either a rancher or an tractor-driver, but not both. How many residents of Dashville are ranchers?

Since each of the 110 residents in Dashville is either a rancher or a tractor-driver, but not both, we have r + t = 110, where r is the number of ranchers and t is the number of tractor-drivers.

(1) There are more than 81 ranchers who reside in Dashville

This implies that r > 81. However, the exact number of ranchers is still unclear. Not sufficient.

(2) The number of ranchers who reside in Dashville is less than three times the number of tractor-drivers who reside in Dashville

This implies r < 3t. Substituting t = 110 - r, we get r < 3(110 - r), which simplifies to r < 82.5. Still, the exact number of ranchers is unclear. Not sufficient.

(1)+(2) Combining the above, we get 81 < r < 82.5. Therefore, r must be 82. Sufficient.

Answer: C.

Hope it's clear.

umangshah · Answer

Let Rangers be X and Tractor drivers be Y.
X+Y=110
We need to find x.

Statement 1: x > 81. Thus x can take any values such as 82,82,83, etc. Thus Insufficient.
Statement 2: x < 3y. There can multiple combinations of numbers which can satisfy this equation and still the sum of x & y equals 110. Thus Insufficient.

Combined 1 & 2: By addition the equations,
  x- 81 > 0 
 -x+3y > 0

3y -81 > 0 
  y>27

Thus we now use x>81 and y>27 and find that only one solution satisfies the equations i.e., x=82 and y =28. Thus sufficient.

Option C is correct.

Each of the 110 residents in Dashville is either a rancher or

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 Data Sufficiency (DS) Questions

Each of the 110 residents in Dashville is either a rancher or

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