In a certain box of of widgets there are only brass widgets and iron

Question

In a certain box of of widgets there are only brass widgets and iron widgets. If 42 of the widgets are brass and 14 are iron, what is the total weight, in kilograms of the box?

(1) The weight of seven brass widgets is three times the weight of an iron widget.
(2) The total weight of a brass widget and five iron widgets is 38 kilograms.

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tgsankar10 · Answer

No of Brass widgets,  B=42  
 No of Iron widgets,  I=14

weight of brass widget,  b  & weight of iron widget,  i

Bb+Ii=? 
 
  Statement 1:    The weight of seven brass widgets is three times the weight of an iron widget.

7b=3i

b=\frac{3}{7}i

Not Sufficient

Statement 2:  The total weight of a brass widget and five iron widgets is 38 kilograms.

b+5i=38

There is only one equation.

Not Sufficient

Statements Combined:

b=\frac{3}{7}i  &  b+5i=38

\frac{3}{7}i+5i=38

i=7  &  b=3

Bb+Ii=(42*3)+(14*7)=126+98=224

Sufficient

Answer: C

Dereno · Answer

Box = 42 Brass (B) + 14 iron (F)

We need to find the weight of the box .

Statement 1:

(1) The weight of seven brass widgets is three times the weight of an iron widget.

7 B = 3 F

Hence, insufficient

Statement 2:

(2) The total weight of a brass widget and five iron widgets is 38 kilograms.

B + 5F = 38

Hence, Insufficient

Combining statements 1 and 2, we get

B = (3/7)*F

(3/7)*F + 5F = 38

38F = 7* 38

F = 7 , then B = 3

Thus, 42 B + 14 F =  42*3 + 14*7 = 224 kg.

Hence, Sufficient

Option C

ManifestDreamMBA · Answer

Let weight of Brass be b and iron be i
42b+14i = ?
14(3b+i) = ?

S1
The weight of seven brass widgets is three times the weight of an iron widget.
7b=3i
b=3i/7
But we don't know i
Insufficient

S2
The total weight of a brass widget and five iron widgets is 38 kilograms.
b+5i=38
But we don't know i or b
Insufficient

Combined, we have 3i/7+5i=38
i=7 and b = 3
Total weight = 42*3+14*7
Sufficient

Answer C

Souradeep17 · Answer

Let weight of Brass widget = B
Let weight of Iron widget= I

Brass widget = 42 and iron widget= 14

we need to find total weight (42B+14I)

option 1 -
7B=3(I) ---eq 1
6* {7B}=6*{3I}
42B=18I
So , we can write total weight as 18I+14I=32I (however we don't know the value of I) . So option 1 Not sufficient alone

Option 2

B+5I=38 --eq 2
B=38-5I
42B=42(38-5I)
total weight will be 
42(38-5I) + 14I=

(again, here we don't know the value of I so alone not sufficient).

Checking both the options together - 
eq 1 and eq 2
7B=3I and B+5I=38
3I/7+5I=38
38I=38*7
I=7, B=3 From here we can find total weight
42*3+7*14=126+98=224
 (option C is correct )

In a certain box of of widgets there are only brass widgets and iron

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GMAT Data Sufficiency (DS) Questions

In a certain box of of widgets there are only brass widgets and iron

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615 to 715 in 15 Days (Ria's Strategies)

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