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605-655 (Medium)|   Geometry|      
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If one of the sides of a large carton that measures 25 inches by 40 24 Feb 2019, 09:43
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E
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45% (medium)

Question Stats:

64% (01:44) correct 36% (01:41) wrong based on 136 sessions

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If one of the sides of a large carton that measures 25 inches by 40 inches by 60 inches is to be increased by 2 inches, what is the greatest possible volume increment, in square inches?

(A) 1,600

(B) 2,000

(C) 2,400

(D) 3,000

(E) 4,800
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E
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If one of the sides of a large carton that measures 25 inches by 40 25 Feb 2019, 05:46
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Volume is length·width·height
We maximise the additional volume by adding it to the shortest side – this way it is multiplied by the largest numbers
Thus, 2·40·60=4800 extra volume
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If one of the sides of a large carton that measures 25 inches by 40 25 Feb 2019, 22:12
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Solution


Given:
In this question, we are given
    • The measures of three sides of a large carton is 25 inches, 40 inches and 60 inches.
    • One of the three sides is to be increased by 2 inches.

To find:
We need to determine
    • The greatest possible volume increment of that carton, in square inches.

Approach and Working:
The volume increase can happen in three possible ways
    • Increasing 25 by 2 and keeping 40 and 60 as constant
    • Increasing 40 by 2 and keeping 25 and 60 as constant
    • Increasing 60 by 2 and keeping 25 and 40 as constant

As the magnitude of the increase is constant, maximum increase will happen when we increase the smallest number and multiply it by the larger two numbers.

Therefore, maximum increase = 2 x 40 x 60 = 4800 square inches

Hence, the correct answer is option E.

Answer: E

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If one of the sides of a large carton that measures 25 inches by 40 26 Feb 2019, 00:59
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rohan2345
If one of the sides of a large carton that measures 25 inches by 40 inches by 60 inches is to be increased by 2 inches, what is the greatest possible volume increment, in square inches?

(A) 1,600

(B) 2,000

(C) 2,400

(D) 3,000

(E) 4,800
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Original area ; 25*40*60 ; 6,00,00
max increase is done by adding 2 inches increase to smallest side i.e 25 here
so increase 4800
IMO E
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If one of the sides of a large carton that measures 25 inches by 40 27 Apr 2020, 23:49
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When two numbers are brought to equal the output is highest.

hence we bring the lowest number rise up, we will see greater number.

Hence, 25+2.

27*40*60 - 25*40*60

Therefore, 40*60(27-25)
= 4800
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If one of the sides of a large carton that measures 25 inches by 40 31 Aug 2021, 17:48
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To get the greatest INCREMENT increase in a product of 3 values, you want to increase the Factor that will result in the GREATEST PERCENTAGE Increase


A percentage increase is always take on the original value. Thus, with a net positive change of +2, the factor with the lowest value will result in the highest percentage increase/increment

25 ——-(+2) ———-> 27

Fractional Increase of: +(2/25) = +(8/100) = + 8% percentage change Increase


Current volume is = (25) * (40) * (60) = (25) * (2400) = 60,000

8% increase of 60,000 volume is

1% is 600

Those 8% is 8 TIMES that amount as an increment increase or:

(8) (600) = 4,800


(E)
4,800

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If one of the sides of a large carton that measures 25 inches by 40 31 Aug 2021, 22:24
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Hey,

The equation for the volume of a rectangular solid is:

V = Length x Width x Height

To decide which side should have the increase in 2" to have the greatest increase in volume, we must see which of the two numbers multiply to the greatest number

It is obvious that 40 x 60 multiply to the greatest number: 2400

That means that it is 25 that must be increased by 2", so that this additional length is multiplied by the greatest possible number to produce the greatest possible increase in volume

To see how much of an increase in volume this will be, set up an equation:

(25+2)(2400) - (25)(2400) =

25(2400) + 2(2400) - 25(2400)

= 2(2400)

= 4800

The answer is E
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If one of the sides of a large carton that measures 25 inches by 40 10 Jun 2023, 05:28
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