Two types of widgets, namely type A and type B, are produced on a mach

Question

Two types of widgets, namely type A and type B, are produced on a machine. The number of machine hours available per week is 80. How many widgets of type A must be produced?

(1) One unit of type A widget requires 2 machine hours and one unit of type B widget requires 4 machine hours.
(2) Every week, at least 10 units of type A widgets and at least 15 units of type B widgets must be produced.

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Purnank · Answer

I think C,
Given - Two types of widgets, namely type A and type B, are produced on a machine. The number of machine hours available per week is 80. 
Assume A as a hours required to produce Type A widget and B as a hours required to produce Type B.

To find how many widgets of type A must be produced lets check given condition.

1st - One unit of type A widget requires 2 machine hours and one unit of type B widget requires 4 machine hours.
Therefore, 2A + 4B = 80
On further solving, A + 2B = 40 ------- (Eq1)
So there will be multiple values for both A & B hence not sufficient.

2nd - Every week, at least 10 units of type A widgets and at least 15 units of type B widgets must be produced.
Therefore A>= 10 and B>=15. Doesnt says anything else. Hence not sufficient.

But now combining both we will see only only A = 10 and B = 15 satisfying values for both A & B. 
Hence C.

SweetVault · Answer

Confused here, How many widgets of type A *must* be produced?

Answer = given in B alone; "Every week, at least 10 units of type A widgets *must* be produced. Therefore, answer = 10

ThatTallGuy · Answer

Given from the problem, we can say that the total time per week for producing A and/or B is 80 hours.
We do not know:
- The number of units required,
- The rate of production for widgets.

(1) We know that it takes 2 hours for one unit of A and 4 hours for one unit of B.  But we do not know the required amount.   Insufficient. 
(2) We know the amount required, but  we do not know the production rate .  Insufficient.

(1) + (2) Combining both, we can get that the maximum amount of widgets that the machine can produce to correspond to the requirements is 10 of A and 15 of B (10*2 + 4*15 = 80). And it is sufficient to answer the question.  Sufficient (C)

egmat · Answer

Hi SweetVault,

I see exactly where this is snagging. You're reading " at least  10 units of type A" as if it fixed type A at  10 . That's the one spot to fix.

"At least  10 " is a  minimum , not a set value. It means A could be  10 , or  11 , or  12 , or  50  - anything from  10  upward. The question asks for  how many A  must  be produced , i.e., a single definite number. A range from  10  up doesn't pin down one number.

Two cases that both obey Statement (2): 
- A =  10 , B =  15 
- A =  11 , B =  20

Both satisfy "at least  10  A and at least  15  B," yet type A is a different number in each. Same statement - two different answers -  Statement (2) alone is not sufficient.

Why C works

Statement (2) alone has no cap stopping A from climbing. What forces A down to exactly  10  is the  80 -hour limit, and that only enters once you bring in Statement (1).

From ( 1 ): each A costs  2  hours, each B costs  4  hours, so  2 A +  4 B ≤  80 . Now apply the minimums from ( 2 ): the smallest possible hours are  2 ( 10 ) +  4 ( 15 ) =  20  +  60  =  80  - that already uses up every available hour. So there's no room to make even one extra widget of either type. A is locked at exactly  10 .

That's the key: the minimum from ( 2 ) plus the ceiling from ( 1 ) squeeze together to a single point. Neither statement does that alone - you need  both , so the answer is  C .

Takeaway for DS: "at least" gives a range, and a range isn't a definite answer unless another constraint closes it off.

Answer: C

Two types of widgets, namely type A and type B, are produced on a mach

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GMAT Data Sufficiency (DS) Questions

Two types of widgets, namely type A and type B, are produced on a mach

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