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# One integer will be randomly selected from the integers 11 to 60, incl

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Math Expert
Joined: 02 Sep 2009
Posts: 51280
One integer will be randomly selected from the integers 11 to 60, incl  [#permalink]

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11 Jul 2018, 23:53
00:00

Difficulty:

25% (medium)

Question Stats:

78% (01:24) correct 22% (01:34) wrong based on 46 sessions

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One integer will be randomly selected from the integers 11 to 60, inclusive. What is the probability that the selected integer will be a perfect square or a perfect cube?

(A) 0.1
(B) 0.125
(C) 0.16
(D) 0.5
(E) 0.9

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Joined: 19 Nov 2017
Posts: 174
Location: India
Schools: ISB
GMAT 1: 670 Q49 V32
GPA: 4
Re: One integer will be randomly selected from the integers 11 to 60, incl  [#permalink]

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11 Jul 2018, 23:57
5/48 = 0.10xx

Should be A
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Regards,

Vaibhav

Sky is the limit. 800 is the limit.

~GMAC

Math Expert
Joined: 02 Aug 2009
Posts: 7112
Re: One integer will be randomly selected from the integers 11 to 60, incl  [#permalink]

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11 Jul 2018, 23:59
Bunuel wrote:
One integer will be randomly selected from the integers 11 to 60, inclusive. What is the probability that the selected integer will be a perfect square or a perfect cube?

(A) 0.1
(B) 0.125
(C) 0.16
(D) 0.5
(E) 0.9

1) check for squares :-
3^2=9 and 8^2=64
so 4^2, 5^2, 6^2 and 7^2 will all give us a perfect square

2) now for cubes
2^3=8, 3^3=27 and 4^3=64
so only one 3^3

total 4+1=5 out of 60-11+1=50 integers

probability = 5/50 = 1/10 =0.1

A
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1) Absolute modulus : http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372
2)Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html
3) effects of arithmetic operations : https://gmatclub.com/forum/effects-of-arithmetic-operations-on-fractions-269413.html

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Joined: 02 Aug 2009
Posts: 7112
Re: One integer will be randomly selected from the integers 11 to 60, incl  [#permalink]

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12 Jul 2018, 00:00
vaibhav1221 wrote:
5/48 = 0.10xx

Should be A

5/48 is not 0.1...
since 11 and 60 are inclusive it will be 5/50
_________________

1) Absolute modulus : http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372
2)Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html
3) effects of arithmetic operations : https://gmatclub.com/forum/effects-of-arithmetic-operations-on-fractions-269413.html

GMAT online Tutor

Manager
Joined: 19 Nov 2017
Posts: 174
Location: India
Schools: ISB
GMAT 1: 670 Q49 V32
GPA: 4
Re: One integer will be randomly selected from the integers 11 to 60, incl  [#permalink]

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12 Jul 2018, 00:12
chetan2u wrote:
vaibhav1221 wrote:
5/48 = 0.10xx

Should be A

5/48 is not 0.1...
since 11 and 60 are inclusive it will be 5/50

My bad, made a silly calculation error to get max outcomes as 48. Plus i did not divide 5/48 any further to get 0.104. Thanks for pointing it out.

Regards,
V
_________________

Regards,

Vaibhav

Sky is the limit. 800 is the limit.

~GMAC

Director
Joined: 31 Oct 2013
Posts: 899
Concentration: Accounting, Finance
GPA: 3.68
WE: Analyst (Accounting)
One integer will be randomly selected from the integers 11 to 60, incl  [#permalink]

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12 Jul 2018, 04:50
Bunuel wrote:
One integer will be randomly selected from the integers 11 to 60, inclusive. What is the probability that the selected integer will be a perfect square or a perfect cube?

(A) 0.1
(B) 0.125
(C) 0.16
(D) 0.5
(E) 0.9

Integer Range : 11 -60. Total no. of Integers = 60 - 11 + 1 = 50

Case 1: Perfect Square:

$$4^2$$ =16
$$5^2$$ = 25
$$6^2$$ = 36
$$7^2$$ = 49

Case 2 : Perfect Cube:

$$3^3$$ = 27

We know that we need to add if it's a OR probability.

$$\frac{4}{50}$$ + $$\frac{1}{50}$$

= $$\frac{5}{50}$$
= $$\frac{1}{10}$$
= 0.1

Thus the best answer is A.
One integer will be randomly selected from the integers 11 to 60, incl &nbs [#permalink] 12 Jul 2018, 04:50
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