12 Days of Christmas GMAT Competition - Day 3: A manufacturer creates

Question

12 Days of Christmas 2024 - 2025 Competition with $30,000 of Prizes

A manufacturer creates an alloy using only copper and tin. What percentage of the alloy is copper by weight?

(1) If the weight of the tin is increased by 50%, the total weight of the alloy becomes 9 kilograms.
(2) If the weight of the tin is increased by 200%, the total weight of the alloy increases by 50%.

Bunuel · Accepted Answer

GMAT Club's Official Explanation:

A manufacturer creates an alloy using only copper and tin. What percentage of the alloy is copper by weight?

Assuming the weight of copper is c and the weight of tin is t, we need to find the value of c/(c + t) * 100.

(1) If the weight of the tin is increased by 50%, the total weight of the alloy becomes 9 kilograms.

This implies c + 1.5t = 9. Without additional information, the exact values of c and t, or their ratio, cannot be determined. Not sufficient.

(2) If the weight of the tin is increased by 200%, the total weight of the alloy increases by 50%.

This implies c + 3t = 1.5(c + t), which simplifies to c = 3t. Substituting into c/(c + t) * 100 gives 3t/(3t + t) * 100 = 75%. Sufficient.

Answer: B.

siddhantvarma · Answer

Let C = weight of copper, T = weight of Tin
We're asked: What percentage of the alloy is copper by weight? => We need (C/C+T)*100

(1) If the weight of the tin is increased by 50%, the total weight of the alloy becomes 9 kilograms.

T => T + 50/100*T => 1.5T
Total weight = C + 1.5T = 9kg
This gives us a relation between C and T, we still can't find the value (C/C+T)*100 from this information alone. 
Therefore, Statement (1) is insufficient

(2) If the weight of the tin is increased by 200%, the total weight of the alloy increases by 50%.

T => T + (200/100)*T => 3T
Total weight = C + 3T
This new weight is actually a 50% increase in the alloy's actual weight
Actual weight = C + T
C+3T = 1.5(C+T) => 2T = 0.5C => C = 4T

We can put C = 4T in (C/C+T)*100 and get 4/5*100 = 80%
Hence this information is sufficient

Therefore, Statement (2) is sufficient => (B)

HarshaBujji · Answer

Let the weight of copper be c and the weight of tin be t.
 The percentage of copper in the alloy is: c/(c+t)*100.

Statement (1): 
If the weight of tin is increased by 50%, the total weight of the alloy becomes 9 kilograms.

c+1.5t = 9. We cannot find the percentage of copper in the alloy using this.

Hence Statement (1) is insufficient.

Statement (2): 
If the weight of the tin is increased by 200%, the total weight of the alloy increases by 50%.

A 200% increase in the weight of tin means the new weight of tin becomes 3t.

Total weight = c+3t.

c+3t = 1.5(C+t) =>  c = 3t

Using Statement (2) we can find the copper percentage I,e 75%. (Sufficient)

Hence IMO B

Kinshook · Answer

A manufacturer creates an alloy using only copper and tin. What percentage of the alloy is copper by weight?

Let the percentage of copper by weight in the alloy be p%
The percentage of tin by weight in the alloy = 100% - p%

Let the total weight of the alloy be x kilograms
Copper weight = xp%
Tin weight = x(100%-p%)

(1) If the weight of the tin is increased by 50%, the total weight of the alloy becomes 9 kilograms.
New tin weight = 1.5x(100%-p%)
Total weight of the alloy = xp% + 1.5x(100%-p%) = 9
xp% + 1.5x - 1.5xp% = 9
1.5x - .5xp% = 9
With the information the value of p% can not be derived
NOT SUFFICIENT

(2) If the weight of the tin is increased by 200%, the total weight of the alloy increases by 50%.
New tin weight = 3x(100%-p%)
Total alloy weight = xp% + 3x(100%-p%) = 1.5x
p% + 3 - 3p% = 1.5
p% = 75%
75% percentage of the alloy is copper by weight
SUFFICIENT

IMO B

kingbucky · Answer

Statement (1): 
- Equation based on statement:  C + T 	imes 1.5 = 9 
- This statement alone does not provide the individual weights of copper or tin, nor does it allow us to directly calculate the ratio  \frac{C}{C+T} . Thus, we cannot determine the percentage of copper solely from this statement.

Statement (2): 
- Rewriting the given condition: Increasing T by 200% means  T_{new} = 3T .
- The total weight of the alloy thus increases by 50%, leading to the equation:  C + 3T = 1.5(C + T) 
- Simplifying the equation gives:  C + 3T = 1.5C + 1.5T 
  1.5C - C + 1.5T - 3T = 0 
  0.5C - 1.5T = 0 
  C = 3T 
- From  C = 3T , the ratio  \frac{C}{C+T}  can be uniquely determined as  \frac{3T}{3T + T} = \frac{3}{4}  or 75%.

Conclusion: 
Statement (1) alone is insufficient, while statement (2) alone is sufficient to determine the percentage of copper in the alloy.

Correct Answer: B

andreagonzalez2k · Answer

c=weight of copper
t=weight of tin

¿100*c/(c+t)?

(1)
c+t+0.5t=9 -> c=9-1.5t
100*(9-1.5t)/(9-0.5t) -> its value depends on t

INSUFFICIENT

(2)
c+t+2t=(c+t)+0.5(c+t)
1.5t=0.5c
c=3t

100*3t/4t= 75%

SUFFICIENT

IMO B

missionmba2025 · Answer

Weight of Cooper = wc

Weight of Tin = wt

Total Weight = wc + wt

Question: wc / (wc + wt)

1) wc + 1.5 wt = 9

Using this additive relationship we cannot find the given ratio. Statement 1 alone is not sufficient.

Eliminate A, and D.

2) wc + 3wt = 1.5(wc+wt)

wc + 3wt = 1.5wc + 1.5wt

0.5wc = 1.5wt

wc = 3wt

As we now have a relationship between wc and wt, we can substitute the same and find a value.

Statement 2 is alone sufficient.

Option B

A_Nishith · Answer

We are tasked with determining the percentage of copper in an alloy made of only copper and tin.

Let the weight of copper be C kilograms and the weight of tin be T kilograms. 
The total weight of the alloy is C+T, and we want to find:

Percentage of copper by weight= C/(C+T)×100.

Analyzing the Statements 
(1) If the weight of the tin is increased by 50%, the total weight of the alloy becomes 9 kilograms.

If T is increased by 50%, the new weight of tin becomes 1.5T. 
The total weight of the alloy then becomes:C+1.5T=9.

The original total weight of the alloy is C+T. 
Using the equation 
C+1.5T=9, we cannot isolate C or T because there is only one equation and two variables. 
Thus, Statement (1) alone is insufficient.

(2) If the weight of the tin is increased by 200%, the total weight of the alloy increases by 50%.

If T is increased by 200%, the new weight of tin becomes 3T. 
The total weight of the alloy increases by 50%, so the new total weight is:
1.5(C+T)=C+3T.

Expanding and simplifying:
1.5C+1.5T=C+3T,
0.5C=1.5T,
C=3T.

This gives a direct relationship between 
C and T, allowing us to calculate the percentage of copper:
3T/(3T+T) = 3/4

Thus, 75% of the alloy is copper. Statement (2) alone is sufficient.

(1) and (2) together: Since Statement (2) alone is sufficient, we do not need to combine it with Statement (1).

Answer: (B)
Statement (2) alone is sufficient, while Statement (1) alone is not.

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