If the total price of n pounds of equally priced cotton was $360, what

Question

If the total price of n pounds of equally priced cotton was $360, what was the average price per pound of the cotton?

(1) Had the average price of the cotton been $1 per pound higher, the total price of n pounds would have been $240 more.
(2) Had the average price of the cotton been $1.2 per pound lower, the total price of n pounds would have been 80 percent less.

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Navdeep2000 · Answer

Let the price per pound of the equally priced cotton be $x.  
 Accordingly, we are given that xn=$360 
 We have to find the average price per pound, i.e. 360/n, which basically is to solve for x.

(1) Had the average price of the cotton been $1 per pound higher, the total price of n pounds would have been $240 more.
 (x+1)n=(360+240) 
 (x+1)n=600 
 xn+n=600

Also, we know that xn=360 
 From here onwards, we do not need to solve to know that it will be  sufficient .  
 (FYI = x will be $1.5)

(2) Had the average price of the cotton been $1.2 per pound lower, the total price of n pounds would have been 80 percent less. 
 (x-1.2)n=0.2(360) 
 xn-1.2n= 72

Again, since we know that xn=360, we do not need to solve further to prove that it's  sufficient .

Option D

Dereno · Answer

Let n be the total number of pounds,

And p be the price per pound.

n * p = 360

We need to find p?

Statement 1:

Had the average price of the cotton been $1 per pound higher, the total price of n pounds would have been $240 more.

n* (p+1) = 360+240

np + n =600

n =240

p = 360/240 =1.5

Sufficient

Statement 2:

Had the average price of the cotton been $1.2 per pound lower, the total price of n pounds would have been 80 percent less.

n * (p-1.2) = 72

360 - 1.2 n = 72

n =240

same as statement 1.  Sufficient

Option D

egmat · Answer

What we know: 
- Total price =  $360  for  n  pounds
- Average price per pound = 360/n (this is what we need to find)

Key insight:  If we can find  n , we automatically know the price per pound.

Statement 1:  Price $1 higher → Total becomes $360 + $240 = $600

Let's call price per pound = p
Then: n = 360/p (since total = n × p = 360)

With the new price (p + 1):
n × (p + 1) = 600

Substituting n = 360/p:
(360/p) × (p + 1) = 600
360 + 360/p = 600
360/p = 240
 p = $1.50

We get one unique value.  SUFFICIENT

Statement 2:  Price $1.20 lower → Total becomes 80% less

80% less means we pay only 20% of original 
New total = 20% of $360 =  $72

With the new price (p - 1.2):
n × (p - 1.2) = 72

Substituting n = 360/p:
(360/p) × (p - 1.2) = 72
360 - 432/p = 72
432/p = 288
 p = $1.50

We get one unique value.  SUFFICIENT

Both statements give us equations with one unknown (p). One equation, one unknown = solvable!

Answer: D

ExpertsGlobal5 · Answer

Explanation:  
 
Let the average price per pound of the cotton be  p .
Since the total price of  n  pounds of cotton was $360:  np  = 360 (Equation I)
  We need to find whether the value of p     can be determined.  
 
 Statement (1) 
 
( p  + 1) n  = 240 +  np  (Equation II)
 
From Equation I and Equation II, we have 2 equations with 2 unknown variables, which can be solved to determine the exact value of  p .   Hence, Statement (1) is sufficient   . 
 
 Statement (2) 
 
( p  – 1.2) n  =  np  – 0.8 np  (Equation III)
 
From Equation I and Equation III, we have 2 equations with 2 unknown variables, which can be solved to determine the exact value of  p .   Hence, Statement (2) is sufficient   . 
 
  D is the correct answer choice.

If the total price of n pounds of equally priced cotton was $360, what

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GMAT Data Sufficiency (DS) Questions

If the total price of n pounds of equally priced cotton was $360, what

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