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.

bumpbot · Answer

Automated notice from GMAT Club BumpBot:

A member just gave Kudos to this thread, showing it’s still useful. I’ve bumped it to the top so more people can benefit. Feel free to add your own questions or solutions.

This post was generated automatically.

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

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

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

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