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# In a basket, the ratio of number of apples to the number of guavas is

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Math Expert
Joined: 02 Sep 2009
Posts: 58464
In a basket, the ratio of number of apples to the number of guavas is  [#permalink]

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29 Aug 2019, 22:52
1
3
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Difficulty:

95% (hard)

Question Stats:

28% (02:55) correct 72% (02:50) wrong based on 53 sessions

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In a basket, the ratio of number of apples to the number of guavas is equal to the ratio of the number of guavas to the number of oranges. If the total number of fruits on the basket is 61, how many guavas are there?

A) 16
B) 20
C) 25
D) 28
E) 30

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Joined: 15 Feb 2018
Posts: 372
Re: In a basket, the ratio of number of apples to the number of guavas is  [#permalink]

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30 Aug 2019, 00:51
61 is prime so I don't believe the question works?

A)16
16: 16: 16 insufficient
32: 16: 8 insufficient
48: 16: 16/3 non-integer and oranges are an integer
64: 16: 4 too many
Can't be A

B) 20
20:20:20 insufficient
40:20:10 too many
Can't be B

C) 25
25:25:25 too many

Can't be C, D or E
Intern
Joined: 30 Aug 2019
Posts: 2
In a basket, the ratio of number of apples to the number of guavas is  [#permalink]

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30 Aug 2019, 01:13
1
Does it work this way?

61 - 25 = 36

36/2 = 18

A:G:O = 18:25:18

Am I correct here?
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In a basket, the ratio of number of apples to the number of guavas is  [#permalink]

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30 Aug 2019, 07:53
Bunuel wrote:
In a basket, the ratio of number of apples to the number of guavas is equal to the ratio of the number of guavas to the number of oranges. If the total number of fruits on the basket is 61, how many guavas are there?

A) 16
B) 20
C) 25
D) 28
E) 30

Project PS Butler

Find the approximate average 61/3 ~ 20

a : g = g : o

Now, If g = 20 (Plugging in option (B) just to check) , a = o = 21 , hence Answer must be (B)
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Joined: 09 Nov 2015
Posts: 138
Re: In a basket, the ratio of number of apples to the number of guavas is  [#permalink]

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30 Aug 2019, 08:36
I have wracked my brains and the only explanation I can come up with is there is a typo in the question and the total number of fruits is 60, not 61. In that case, the number of guavas is 20 which satisfies the condition g^2 = a*o where g, a and o are the numbers of guavas, apples and oranges respectively: (20)^2 = 20*20. Answer is that case would be B.
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In a basket, the ratio of number of apples to the number of guavas is  [#permalink]

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Updated on: 30 Aug 2019, 23:25
2
given
a/g=g/o
g^2=a*0 ; g=√a*o
and a+g+o=61
we need to find g
g=√a*o
only possible when a=o and since fruits max is 61 least value of a & o has to be 25,16 in that case g= 20
IMO B

Bunuel wrote:
In a basket, the ratio of number of apples to the number of guavas is equal to the ratio of the number of guavas to the number of oranges. If the total number of fruits on the basket is 61, how many guavas are there?

A) 16
B) 20
C) 25
D) 28
E) 30

Project PS Butler

Originally posted by Archit3110 on 30 Aug 2019, 10:53.
Last edited by Archit3110 on 30 Aug 2019, 23:25, edited 1 time in total.
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Re: In a basket, the ratio of number of apples to the number of guavas is  [#permalink]

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30 Aug 2019, 23:11
Archit3110

I don't think this works. The question states that the TOTAL number of fruits in the basket is 61 and not, as you have assumed, the MAXIMUM.
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Re: In a basket, the ratio of number of apples to the number of guavas is  [#permalink]

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30 Aug 2019, 23:17
1
Got it.
The ratio is a fraction

20 Guavas

5/4g:g:4/5g
25:20:16
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Re: In a basket, the ratio of number of apples to the number of guavas is  [#permalink]

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30 Aug 2019, 23:26
effatara wrote:
Archit3110

I don't think this works. The question states that the TOTAL number of fruits in the basket is 61 and not, as you have assumed, the MAXIMUM.

effatara edited..

Posted from my mobile device
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Re: In a basket, the ratio of number of apples to the number of guavas is  [#permalink]

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30 Aug 2019, 23:49
@phillipssonicare

Great work! Don't understand how I missed that particular combination!
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Re: In a basket, the ratio of number of apples to the number of guavas is  [#permalink]

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31 Aug 2019, 19:41
effatara wrote:
@phillipssonicare

Great work! Don't understand how I missed that particular combination!

Doesn't mean I actually know how to solve it though!
My algebra got stuck at g=√a√o and trial and error isn't a great approach (especially when random inspiration comes 24 hours later!)
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In a basket, the ratio of number of apples to the number of guavas is  [#permalink]

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31 Aug 2019, 22:19
Number of fruits are in a GP.
$$a+ak+ak^2=61$$
$$a(1+k+k^2)=61$$
assume k=x/y
$$a(1+\frac{x}{y}+\frac{x^2}{y^2})$$=61
$$\frac{a}{y^2}(x^2+y^2+xy)=61$$
As a is an integer and 61 is a prime number,$$\frac{a}{y^2}$$ must be equal to 1.

We get
$$x^2+y^2+xy=61$$
$$(x+y)^2=61+xy$$
x=5 and y=4
or x=4 and y=5

x/y=4/5 or 5/4

Case 1
When x/y=4/5
number of apples=5^2=25
number of guavas=25*4/5=20

Case 2-
When x/y=5/4
number of apples= 4^2=16
number of guavas
= 16*5/4=20

B

Bunuel wrote:
In a basket, the ratio of number of apples to the number of guavas is equal to the ratio of the number of guavas to the number of oranges. If the total number of fruits on the basket is 61, how many guavas are there?

A) 16
B) 20
C) 25
D) 28
E) 30

Project PS Butler

Director
Joined: 24 Nov 2016
Posts: 643
Location: United States
Re: In a basket, the ratio of number of apples to the number of guavas is  [#permalink]

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14 Oct 2019, 06:08
1
Bunuel wrote:
In a basket, the ratio of number of apples to the number of guavas is equal to the ratio of the number of guavas to the number of oranges. If the total number of fruits on the basket is 61, how many guavas are there?

A) 16
B) 20
C) 25
D) 28
E) 30

$$\frac{a}{g}=\frac{g}{o}…g^2=ao…g=\sqrt{ao}…a>g>o$$
$$g=\sqrt{ao}=integer…{ao}=perfectsquare$$
$$perfectsquares:1,4,9,16,25,36,49,64$$
$$a+g+o=61…a>g>o…a≥61/3≥20…a=(25,36,49)…o=(1,4,9,16)$$
$$a=25…o=16…g=\sqrt{25*16}=20…a+g+o=25+20+16=61…only.valid.case$$

Re: In a basket, the ratio of number of apples to the number of guavas is   [#permalink] 14 Oct 2019, 06:08
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