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09 May 2020, 06:50
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C
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
45%
(medium)
Question Stats:
53% (01:13) correct
47%
(01:51)
wrong
based on 59
sessions
History
Date
Time
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Not Attempted Yet
A right circular cone has height H and radius R. A small cone is cut off at the top by a plane parallel to the base. At what height above the base, the section has been made?
1) H = 20 cm
2) Volume of small cone: volume of large cone : 1:64
1) H = 20 cm
2) Volume of small cone: volume of large cone : 1:64
Source: www.GMATinsight.com
09 May 2020, 08:04
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Answer is Option E
Let height and radius of smaller cone: h and r
Let radius of bigger cone: R
1. H=20, no information about h. Insufficient
2. r^2h/R^2H= 1/64. Insufficient
Combining 1 and 2, we can't calculate h as relation between r & R is not given.
Thanks
Let height and radius of smaller cone: h and r
Let radius of bigger cone: R
1. H=20, no information about h. Insufficient
2. r^2h/R^2H= 1/64. Insufficient
Combining 1 and 2, we can't calculate h as relation between r & R is not given.
Thanks
09 May 2020, 08:23
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GMATinsight
if we assume the small cone has height h and raduis r
hence, we can say h/H = r/R
S1: H = 20
no info regarding other variables, hence, not sufficient
S2: (1/3 x pie x r^2 x h): (1/3 x pie x R^2 x H) = 1: 64
or, (r^2 x h)/(R^2 x H) = 1/64
or, (r/R)^2 x (h/H) = 1/64
replacing r/R = h/H, we get (h/H)^3 = (1/4)^3
or, h/H = 1/4
but we don't know H, hence, we cannot determine h
Combining S1 & S2,
we know H = 20 and h/H = 1/4
hence, we can determne h
Together the statements are sufficient (option C)
