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12 Days of Christmas GMAT Competition - Day 6: A business exports

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bellsprout24

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Answer is C. Both statements together are sufficient

1) We know A = 150 and B = 150. We know X = 200 and Y (defined as countries not X) = 100. But on its own this is still insufficient.
2) On its own this is insufficient.
1&2) Now we know if there were 50 units of B exported to Y, then there were 100 units of B exported to X, and 100 units of A exported to X as well to equal 200. 100 units of A to X is twice the 50 units of B to Y. We also know there must have been 50 units of A exported to Y, and 50 + 50 = 100. Both statements together are sufficient.

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Given:
1. There are 2 products - A and B
2. A total of 300 units were exported yesterday

Statement 1:
Units of product A exported = 150 (0.5*300)
So, Units of product B exported = 150

Since one-third of the units exported yesterday were exported to countries other than Country X
Units exported to countries other than Country X = 1/3 of 300 = 100
Product A = 1/3 * 150 = 50
Product B = 1/3 * 150 = 50

Units exported to country X
Product A = 150-50 = 100
Product B = 150-50 = 100

Hence, this is sufficient

Statement 2:
Product A (exported to country X) = twice of units of B exported to other countries

This is insufficient

Hence, the correct answer is A

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A business exports 2 products, A and B. If 300 total units of these 2 products were exported yesterday, what fraction of the product B units were exported to Country X?

(1) Half of the units exported yesterday were product A, and one-third of the units exported yesterday were exported to countries other than Country X.
(2) Yesterday, there were twice as many units of product A exported to Country X as there were units of B exported to other countries.

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Bunuel

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Analyze Statement (1)

Information:
- Total units exported: 300
- Product A units: 300 * 1/2 = 150 units
- Units exported to other countries: 300 * 1/3 = 100 units
Missing Information:
- We don't know the breakdown of Product B exports to Country X and other countries.

	Product A	Product B
Exported to X			200
Exported to Other			100
	150	150	300

Conclusion: Insufficient to determine the fraction of Product B units exported to Country X.

. Analyze Statement (2)

Information:
- Product A units to Country X = 2 * Product B units to other countries
Missing Information:
- We don't have the total number of units for either Product A or B.
- We don't know the total exports to Country X or other countries.

	Product A	Product B
Exported to X	2x
Exported to Other		x
			300

Conclusion: Insufficient to determine the fraction of Product B units exported to Country X.

3. Combine Statements (1) and (2)

	Product A	Product B
Exported to X	2x		200
Exported to Other		x	100
	150	150	300

Conclusion: Option C

Sufficient to determine the fraction of Product B units exported to Country X.

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Please refer to reference image for better understanding

Given: Total units = 300. Find fraction of B exported to X

Statement 1: A = 150, B = 150. 200 units to X, 100 to others. No split info for B. Insufficient.

Statement 2: Relates A and B but no values. Insufficient.

Combine: From (1), A = 150, B = 150. From (2), X_A + X_B = 200 and X_A = 2(150 - X_B). Solve: X_B = 100.

Fraction = 100/150 = 2/3.

Answer: C.

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Let A and B be products A and B respectively.
Let Ax and Bx be the number of products exported to country X.

A + B = 300

We need to find -

(Bx)/B

STATEMENT 1-

This tells us that A = B = 150. So we have B

This also tells us that total units exported to country X = 200

But we still do no know how many of these 200 were product B, hence we don’t know Bx.
INSUFFICIENT

STATEMENT 2 -

This tells us that

(Ax) = 2(B-(Bx))

But we don’t know B or (Bx) to calculate our ratio. INSUFFICIENT

STATEMENT 1 and 2 COMBINED -

From 1, we have

(Ax) + Bx = 200

From 2,

(Ax) = 2(B-(Bx))

Combining,

2(150-(Bx))+(Bx)) = 200

300 - (Bx) = 200

Bx = 100

Ratio -

100/150

2/3
SUFFICIENT

FINAL ANSWER - Option C

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24 Dec 2024, 05:13

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Statement 1 is not sufficient
2 is not sufficient
Combing them we can get the equation in one variable and find out the answer. no need to solve completely

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Problem Recap:

Total Units Exported: 300 (Products A and B)
Goal: Find the fraction of Product B units exported to Country X.

Understanding the Statements:
Statement (1):
Half of the units exported yesterday were Product A, and one-third of the units exported yesterday were exported to countries other than Country X.

Calculate Products A and B:
- Product A: 1/2 × 300 = 150 units
- Product B: 300 − 150 = 150 units
Units Exported to Other Countries:
- Total to Others: 1/3 × 300 = 100 units
- But: We don’t know how these 100 units are split between Product A and B.

Conclusion: Not enough information to find how many Product B units went to Country X.
Statement (2):
Yesterday, there were twice as many units of Product A exported to Country X as there were units of B exported to other countries.

Set Up the Relationship:
- Let B_O = Product B exported to other countries.
- Then, A_X = 2 × B_O
But: Without knowing the total Product A or B exports, we can’t determine the exact numbers.

Conclusion: Not enough information on its own.
Combining Both Statements:

From Statement (1):
- Product A: 150 units
- Product B: 150 units
- Total to Others: 100 units
From Statement (2):
- A_X = 2 × B_O
- Also, A_X + A_O = 150 (since Product A total is 150)
Solving Together:
- A_X + A_O = 150
- A_X = 2 × B_O
- A_O + B_O = 100
Substitute A_X:
2 × BO + AO = 150
AO = 100 − BO
2 × BO + (100 − BO) = 150 ⇒ BO = 50
- Product B to Country X: 150 − 50 = 100 units
- Fraction: 100/150 = 2/3

Conclusion: Both statements together provide enough information to find the fraction.

Final Answer:
C) BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked, but NEITHER statement ALONE is sufficient to answer the question asked.

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Evaluating statement 1 alone:
(1) Half of the units exported yesterday were product A, and one-third of the units exported yesterday were exported to countries other than Country X.
Not sufficient as we do not know that out of the goods exported to country X, what is the breakup between the products A and B.

Evaluating statement 2 alone:
(2) Yesterday, there were twice as many units of product A exported to Country X as there were units of B exported to other countries.
Not sufficient as we do not know that out of the total goods exported, how many were exported to country X.

Evaluating both together:
Combining both the statements, we know that Product A and B exported 150 products each. out of the 300 products, 100 were exported to other than X and 200 were exported to X. We also know that "there were twice as many units of product A exported to Country X as there were units of B exported to other countries" Let the number of units of B exported to other countries be "x".Here we can form an equation for the number of items exported to other than X:
100 = x + (150 - 2x)
Solving we get x = 50. that means out of 150 B items, 100 be exported to Country X

Answer could be C here

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A=units of product A
B=units of product B
X=units exported to Country X
Y=units exported to another Country

AX=units of product A exported to Country X
BX=units of product B exported to Country X
AY=units of product A exported to another Country
BY=units of product B exported to another Country

A+B=X+Y=300

¿BX/B?

(1) A=150, Y=100
B=150, X=200

There are mutiple solutions for BX

INSUFFICIENT

(2) AX=2BY

Clearly insufficient

INSUFFICIENT

(1)+(2)

X=2BY+BX=200
Y=AY+BY=100

BX-2AY=0 -> BX=2AY

A=2BY+AY=150
B=BX+BY=150 -> 2AY+BY=150

-3AY=-150 -> AY=50

BX=2AY=100

BX/B=100/150=2/3

SUFFICIENT

IMO C

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A business exports 2 products, A and B. If 300 total units of these 2 products were exported yesterday, what fraction of the product B units were exported to Country X?

Given: A+B = 300
Find: Bx/B (Unit of B exported to country X/ Total units of B exported)
In this case, we rewrite the given info in a more descriptive format => Ax + Ao + Bx + Bo = 300 (Ax = Units of A to Country X, Ao = Units of A to Other countries and so on)
To find the Bx/B we will need values of Bx and B

Statement:1 Half of the units exported yesterday were product A, and one-third of the units exported yesterday were exported to countries other than Country X.
A = 150 = Ax + Ao
B = 150 = Bx +Bo
Other units = (1/3)*300 = 100 units = Ao +Bo
So to country X = 200 units = Ax +Bx
From this info, we can't get the value of Bx so [Not Sufficient]

(2) Yesterday, there were twice as many units of product A exported to Country X as there were units of B exported to other countries.
Given = A+B = 300 => => Ax + Ao + Bx + Bo = 300
Ax = 2 Bo
2Bo+Ao + Bx +Bo = 300
3Bo +Ao+Bx = 300
I still can't get the desired values from the info in statement 2 [Not Sufficient]

Together:
Ax +Bx = 200
Ax = 2Bo
2Bo + Bx = 200
we know Bo + Bx = 150
so Bo = 50
Bx = 100
Ratio = 100/150
Ratio Bx/(Bx+Bo) can be calculated [Together Suff : Ans C]

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units A + units B = 300

question: units B to X/units B

(1)
It is possible to deduce that:

units A = 150
units B = 150
units to X = 200
units to other = 100

But there is not an unique solution

Condition (1) is insufficient

(2)

units A to X = 2 * units B to other

There is not an unique solution

Condition (2) is insufficient

(1)+(2)

units A = 150 = units A to X + units A to other
units B = 150 = units B to X + units B to other
units to X = 200 = units A to X + units B to X
units to other = 100 = units A to other + units B to other
units A to X = 2 * units B to other

Solving there is an unique solution:
units B to X/units B = 100/150

Conditions (1)+(2) are sufficient

Answer C

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IMO C

Given:
• Total units exported (A + B) = 300
Statement (1):
Half of the units exported yesterday were product A, and one-third of the units exported yesterday were exported to countries other than Country X.
From this statement, we can deduce:
• Units of product A: 0.5×300=150
• Units of product B: 300−150=150
One-third of the total units were exported to countries other than Country X:
• Units exported to countries other than Country X: 1/3×300=100
This means the units exported to Country X: 300−100=200
However, this statement does not provide the specific breakdown of how many units of product B were exported to Country X. It only gives us the total number of units exported to Country X and the total number of units of each product. Therefore, statement (1) alone is not sufficient to determine the fraction of product B units exported to Country X.
Statement (2):
Yesterday, there were twice as many units of product A exported to Country X as there were units of B exported to other countries.
Let's denote:
• AX as the units of product A exported to Country X
• BX as the units of product B exported to Country X
• BO as the units of product B exported to other countries
From the statement, we have :AX=2BO
This statement alone does not provide the total number of units of product A or product B, nor does it provide the total number of units exported to Country X or other countries. Therefore, statement (2) alone is not sufficient to determine the fraction of product B units exported to Country X.
Combining Statements (1) and (2):
From statement (1), we know:
• Units of product A: 150
• Units of product B: 150
• Units exported to countries other than Country X: 100
• Units exported to Country X: 200
From statement (2), we know:AX=2BO
Since 100 units were exported to countries other than Country X, and all units of product B exported to other countries are BO, we have:BO+AO=100where AOis the units of product A exported to other countries.

Now we calculate the units of product B
Conclusion:
Both statements together are sufficient to determine the fraction of product B units exported to Country X. Therefore, the correct answer is:
(C) Both statements together are sufficient.

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24 Dec 2024, 06:47

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Quote:

A business exports 2 products, A and B. If 300 total units of these 2 products were exported yesterday, what fraction of the product B units were exported to Country X?

(1) Half of the units exported yesterday were product A, and one-third of the units exported yesterday were exported to countries other than Country X.
(2) Yesterday, there were twice as many units of product A exported to Country X as there were units of B exported to other countries.

In this case I usually like to draw a little table

	A	B	Total
To country X		x
To other Countries		y
Total			300

we basically need to see if we can calculate x/(x+y)
1)

	A	B	Total
To country X		x	200
To other Countries		y	100
Total	150	150	300

no path on calculating split of 150 into x and y. Not sufficient
2)

	A	B	Total
To country X	2y	x
To other Countries		y
Total			300

Not sufficient either from the table

Combining (1) and (2), however, we can calculate 150 + 200 - 2y + y = 300
-> -y = -50
y = 50

Therefore choose C

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A = number of units of product A exported
B = number of units of product B exported
Bx= number of B units exported to Country X
Bo= number of B units exported to other countries
Ax= number of A units exported to Country X
Ao= number of A units exported to other countries

A+B = 300

1 ->

A = 150
Total units exported to other countries = 300

Units to X =300−100=200
Now, to simplify this,
Ax+Bx= 200 and Ao+Bo =100
Ax+Ao = 150

We cant find Bx/B with this info

2->

Ax = 2Bo
A + B = 300
Ax+Ao = A and Bx+Bo = B

We cant find Bx/B with the given info

Lets combine 1 and 2

A=150, B = 150, Ax+Bx = 200
From 2 => Ax = 2Bo

Ax+Ao = 150 and Bx+Bo = 150 (Since A=150)
=> 2Bo+Ao=150 and Bx = 150-B0 (Ax=2Bo)

From 1 -> Ax+Bx=200,
Substitute Ax=2Bo and Bx=150- Bo
2Bo + (150-Bo)=200
Bo=50

Ax=2Bo = 100 and Bx = 150-Bo=100
Thus,
Bx/B = 100/150 = 2/3

C. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient

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Let:
[*]x = units exported to Country X.
[*]y = units exported to other countries.

A+B=300

Q: Bx = ?

Statement (1):

[i]A=150 & B=150[/i]

One-third of the total were exported to other countries, so two[i]-third of the total were exported to to Country X.[/i]
[i]Ax+Bx=200[/i]

Not sufficient

Statement (2) :
Ax = 2By

[i]Not sufficient [/i]

[i]Statement (1) + Statement (2) :
Ax+Bx=200 and Ax = 2By [/i]

[i]2By+Bx=200 [/i]
[i]2(150-Bx)+Bx=200. ; (B=Bx+By=150)[/i]
300-Bx=200
Bx=100

Sufficient , Ans is C

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24 Dec 2024, 08:33

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Ask : What is fraction of B (B/300) exported to country X ?

Statement 1 - 150 were product A, \frac{[}{fraction]2/3[fraction]} exported to country X

We donot know how many B were exported to country X

Statement 2 - B other countries = 2 * A to X

Not sufficient

Together :

Total = A to X + A to other + B to X + B to others = A to X + A to other + B to X + 2 * A to X

Total other = 2 * A to X + A to other = 100

Total = A to X + 100 + B to X

We cannot find out to B to X

Not sufficient

OPTION E

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24 Dec 2024, 08:35

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Let BX be B exported to X
AX be A exported to X
BO be B exported to Other countries
AO be A exported to Other countries

Total = 300 = AX + AO + BX + BO. We need to calculate BX

A) Half of total is A, ie AX + AO = 150
& Export to other countries = 2/3 * 300 = 200 = AO + BO

Not Sufficient

B) AX = 2*BO

Not Sufficient

C) Using all the eqns from A and B
AX + AO + BX + BO = 300 -----(a)
AX + AO = 150 ------(b)
AO + BO = 100 ------(c)
AX = 2*BO ------(d)

Use b, c, d
150-AX + AX/2 = 100
AX = 100

BX + BO = 150 => BX = 100
Sufficient

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24 Dec 2024, 08:43

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This is nicely solved with a table (attached), where we get the general split between A:B and country X: non X from point (1).
And then, from point (2), we get that A[X] = 2 * B[Not X], which I denoted as 2n and n.

Unless we combine the two pieces of information, there's no way of getting B[X]. However, with two points above, we get $B[X] = 200-2n = 150-n$, which means $n=50$ and from there we calculate B[X].
So, the answer is C.

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photo_2024-12-24_16-39-31.jpg [ 139.07 KiB | Viewed 475 times ]

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A(x) + A(not x) + B(x) + B(not x) = 300 ----- {1}

Statement 1:
A(x) + A(not x) = 150
So,
B(x) + B(not x) = 150----- {2} => Denominator

Also,
A(not x) + B(not x) = 100
So,
A(x) + B(x) = 200----- {3}

Since we have 3 equations for 4 variables, B(x) cannot be solved. Hence, statement 1 is insufficient

Statement 2:

2B(not x) = A(x)----- {4}

Using equations 1 and 4, B(x) cannot be solved. Hence, statement 2 is insufficient

Both:
Using all 4 equations above, we get A(x) + A(not x) + B(x) + B(not x) = 300 - {1}
Substituting A(x) in {3}
We get 2B(not x) + B(x) = 200

From {1}, we have B(x) + .... = 150

Therefore, we have
B(not x) + 150 = 200
B(not x) = 50

B(x) = 100

Ratio = 100/150

Both statements together are sufficient

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