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

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23 Dec 2024, 11:28

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It's a Sets Question
I solve it usually by Matrix Method

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Rohan271

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Don't Know whether it is right approach or not..

	Product A	Product B
Export to country X
Exports to country other than X
			300

(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.

	Product A	Product B
Export to country X			200
Exports to country other than X			100
	150	150	300

This is not sufficient as we cannot have a clear value

(2) Yesterday, there were twice as many units of product A exported to Country X as there were units of B( let this be Y) exported to other countries.

	Product A	Product B
Export to country X	2Y
Exports to country other than X		Y
			300

This is not sufficient as we cannot have a clear value

Combining both the statements, we get value of products B exported to X = 100/200=1/2

hence sufficient

Bunuel

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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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sushanth21

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23 Dec 2024, 11:51

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C
[*]A: Number of units of product A exported.
[*]B: Number of units of product B exported.
[*]AX: Number of units of A exported to Country X
[*]BX: Number of units of B exported to Country X

A + b = 300
(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 = 300/2 = 150, B = 300 - A = 150

Units to other countries = 300/3 = 100
units to X = 300-100 = 200

Ax + Bx = 200, A - Ax + B - Bx = 100

150 - Ax + 150 - Bx = 100
300 - (Ax + Bx) = 100
Ax + Bx = 200

Insufficient

(2) Yesterday, there were twice as many units of A exported to Country X as there were units of B exported to other countries

Let Bo be the units of B exported to otehr countries

Ax = 2 Bo
we know that
Ax + Bx = 200, A-Ax+B-Bx = 100
from A =150, B =150 and Ax = 2Bo

150 - Ax + 150 - Bx = 100
300 - (Ax + Bx) = 100
Ax + Bx = 200

Ax = 2Bo

2Bo + Bx = 200

We also know that, B-Bx = Bo
150 - Bx = Bo
Bx = 150 - Bo

substitute Bx = 150 - Bo into 2Bo + Bx = 200
we get Bo = 50
Bx = 150 - Bo
Bx = 100

Bx/B = 100/150 = 1/3
insufficient alone, But (1) and (2) together are sufficient

Bunuel

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23 Dec 2024, 12:22

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From statement 1 we can tell that the total units exported were 300 with A accounting for 150 and B 150. We can also tell that the total export to X was 200 units but cannot tell how much of this was product B hence insufficient
From statement 2 the comparison is between product A to X and B to other countries which is not relevant to what we need hence insufficient
Combining the two still does not yield any meaningful information that would be of help to us hence E

Bunuel

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23 Dec 2024, 13:29

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Hi everyone

given:
A+B=300
Ax+Bx=Tx (Country X)
Ao+Bo=To (other countries)

[?] [Bx][/B]
1 values = Sufficient
2 Values = Insufficient

(1) 1/2 of 300=150=A=B , 1/3 of 300=100=To -> Tx=200
Let's try 2 cases
Case 1:
A = 150 Ax=100 Ao=50
B = 150 Bx=100 Bo=50
Bx/B= 100/150 = 2/3

Case 2:
A = 150 Ax=125 Ao=25
B = 150 Bx=75 Bo=75
Bx/B= 75/150 = 1/2

[ltr]2 values = Insufficient

(2) Ax = 2*Bo
Let's try 2 cases
Case 1:
A = 150 Ax=100 Ao=50
B = 150 Bx=100 Bo=50
Bx/B= 100/150 = 2/3
Case 2:
A = 200 Ax=175 Ao=25
B = 100 Bx=50 Bo=50
Bx/B= 50/100 = 1/2

(1)+(2) given:
Ax = 2*Bo
1/2 of 300=150=A=B
1/3 of 300=100=To -> Tx=200
The only scenario is:
A = 150 Ax=100 Ao=50
B = 150 Bx=100 Bo=50
Bx/B= 100/150 = 2/3
Sufficient
[/ltr]

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23 Dec 2024, 13:33

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Bunuel

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1. Based on the information given in Statement 1, we can have multiple possible values as shown below -

The statement hence is not sufficient.

2. The information is not sufficient to find the ratio. Eliminate B

Combined

We can find the value of x.

Sufficient to answer the question.

Option C

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23 Dec 2024, 14:14

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1. Total=300
A=150, B=150
A Other + B other = 100.
This distribution is required. NOT SUFFICIENT

2. A other : B other = 2:1..NOT SUFFICIENT

Together,

150-2x+x=100
x=50

so B to X= 150 -x=100

Answer C

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23 Dec 2024, 16:11

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300 = A + B
Bx = products B exported to country X
Bt = total products B exported to whole world

Q: Bx /Bt

(1) A= 1/2T & 1/3T = World except X

Here we can infer then that, 1/2T = B and that 2/3T were exported to country X but we can't tell wether how much of the 2/3T were from exports of product A or B. Insufficent

(2) Exports to country X = Ax + Bx -> Ax = 2Bx Thus X = Ax + 2Ax = 3Ax but still we can't tell how many from the total were exported to country X.

(C) Combined we have sufficient information to know the proportion of products A/B exported to country X & the proportion of products exported to X and the rest of the countries. Sufficient

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23 Dec 2024, 16:54

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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.

We need to know the relationships between the number of products sold to country X and the proportion of products B in those products exported to X, thus only by combining both statements we'd get that information. Correct answer is (C)

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23 Dec 2024, 18:05

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A: Z
B: 300-Z.
Other countries: Y
Country X: 300-Y
Find how many of 300-Z are exported to X.
This is a matrix problem (Unfortunately I couldn't put the picture here)

(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.
Z=300/2=150.
300/3=100 exported to other countries. So 200 is exported to X. If we found how many of this 200 is in A or B, we could calculate. So insufficient.

(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.--->
B exported n amount of units to other countries, A exported 2n to X. But we don't know anything about B. insufficient.

1+2) ---->
A=150 so B=150.
If B export n units to other countries, it exports 150-n to X.
If A exports 2n units to X, when add the two together, 150-n+2n=200.
n=50. We can calculate the necessary amount through these.
So two together are sufficient. C is correct

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23 Dec 2024, 18:20

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A+B = 300; How many B are 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.

A = 150; 2/3rd to country x = 100;
B = 150; but out of these 150 how many exported to x is not given and can't be calculated.

(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.

Here also some relation is given, but without any absolute value we can't calculate required thing.

now by combining both the statement, we can say that:

Product a to x = (2*50) = 50 (units of b exported to other countries)

Hence b to x were 150-50 = 100.

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Given:

Total units exported: 300

On analyzing option A,

Total units exported to countries other than X: 1/3*300=100 , which means
Total units exported to country X = 300-100=200

From this:

No of Product A units exported=1/2*300=150
No of Product B units exported=1/2*300=150

However just by this statement alone we cannot individually determine the split of Product A & B units sold in Country X & outside Country X. Thus, A alone is insufficient & is option D & both can hence be eliminated.

---

On analyzing option B,
Let the number of exports of B to other countries be x & the exports to A be hence 2x. This individually does not help us determine the individual split of the items to country X & countries outside country X & hence is insufficient to answer the given question.

Statement B alone is insufficient & hence can be eliminated.

---

On Combining both statements, we have the following information:

Total units exported to countries other than X: 1/3*300=100 , which means
Total units exported to country X = 300-100=200

From this:

No of Product A units exported=1/2*300=150
No of Product B units exported=1/2*300=150

Let the number of exports of B to other countries outside X be x & the exports to A be hence 2x.

So the exports of B to country X would be (150-x) & exports of A to countries outsid X would be (150-2x)

150-2x+x=100 ( Exports outside Country X on subsitution of the values given above)

x=50

Hence the breakdown is as follows

Product A

Country X-100
Outside X-50

Product B

Country X-100
Outside X-50

Hence the fraction of the product B units exported to Country X is 100/300=1/3
---

Final Answer:

(C) Both statements together are sufficient.

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23 Dec 2024, 22:27

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	Product A	Product B	Total
Country X		x
Not Country X
Total		y	300

To find, x & y for the fraction

i)

	Product A	Product B	Total
Country X		x	200
Not Country X			100
Total	150	150	300

No idea about x, eliminate

ii)

	Product A	Product B	Total
Country X	2a	x
Not Country X		a
Total		y	300

No info on x & y, eliminate

i + ii)

	Product A	Product B	Total
Country X	2a	200-2a / 150 - a	200
Not Country X	100-a	a	100
Total	150	150	300

200 - 2a = 150 - a
50 = a

x = 100 & y = 150

IMO C

Bunuel

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Let the number of B units exported to country X be b.

(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.
We can't solve for the fraction of the product B units that were exported to 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.
We can't solve for the fraction of the product B units that were exported to Country X

Both (1) & (2):

	A	B
X	200 - b	b	200
not X	b - 50	150 - b	100
	150	150	300

From (2), we also have 200 - b = 2 x (150 - b)
We can solve for b and therefore the fraction of the product B units that were exported to Country X.

Answer: C

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Bunuel

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2 products are A and B, totally 300 units (E) of (A + B) were exported yesterday.
Fraction of B exported to Country X is ?

Statement 1:
1/2(E) = A; 1/2*(300) = 150 units of A, which essentially means 150 units of B were also exported

1/3(E) = countries other than X = 1/3*(300) = 100 units, which means exports to Country X = 200 units

From this, we can get a few combinations of exports that can be found:

Country/Product	Product A	Product B
Country X	100	100
Other Countries	50	50

Country/Product	Product A	Product B
Country X	150	50
Other Countries	0	100

Country/Product	Product A	Product B
Country X	50	150
Other Countries	100	0

Since multiple answers are possible, this statement is not sufficient.

Statement 2:
Product A to Country X = 2 * Product B to other countries

This does not give us the relationship between Product B and Country X, so this statement is not sufficient as well.

Statement (1) + (2)

Country/Product	Product A	Product B
Country X	100	100
Other Countries	50	50

We can get only these values that satisfy all the conditions. Hence the fraction of Product B to Country X is 100/300 = 1/3

[C] is the correct answer. Both statements (1) and (2) are required.

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Bunuel

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Country/Product	Product A	Product B
Country X	100	100
Other Countries	50	50

Country/Product	Product A	Product B
Country X	150	50
Other Countries	0	100

Country/Product	Product A	Product B
Country X	50	150
Other Countries	100	0

Country/Product	Product A	Product B
Country X	100	100
Other Countries	50	50

We can get only these values that satisfy all the conditions. Hence the fraction of Product B to Country X is 100/300 = 1/3

[C] is the correct answer. Both statements (1) and (2) are required.

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23 Dec 2024, 23:46

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St 1 - not sufficient on its own
St 2 not sufficient on its own

Combined:
If we make a table then we can see that 2x+100-x=150 so we can find the value of X which is b going to other countries and 100-X will give probability of B going to country X

Ans C

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23 Dec 2024, 23:47

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I would say, answer C

We need statement one in order to determine the number of A products exported and the number of product B exported (150 each)

We need statement two to determine the fraction of product B exported to country X

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24 Dec 2024, 00:04

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Hi All,

Given A+B=300

Statement 1,

gives us 150 each of A and B were exported yesterday,

and 2/3 rd of units were exported to country X.

But we dont know what propotion was sent to country x, it could be all 100 A untis 100 B units or 150 A units and 50 B units,

In-sufficient

Statement 2,

We dont know how much export was sent to other countries as well as to country X

In-sufficient

Statement 1 + 2

From S1 we get 2/rd of 300 was sent to X and from S2 we get that A for X is double the B for other countries

So if we create a ration Ax:Bx=100:100 and Ao:Bo=50:50,

But if we change the value of Ax and Bo the statement 1 will be faslified as then the total for X wont be 2/3 of all export.

Hence C is the answer