A juice manufacturer organized taste-testing sessions featuring four

total number of people is T
61% of T is an integer --> T is a multiple of 100
31.5% of T is an interger --> T is multiple of 200

C+D = 8.5% * T = 65 + x

After here i looked at the answer choices and found 20. it is satifying both conditions...

Answer D

I get D, but I'm not sure that my method is sound.

You have A + B + C + D = total testers. Stating the variety they think is most similar to freshly squeezed orange juice means each person should get 1 vote.

x = total number of testers

A + B + C + D
.61x + (.5)(.61x) + 65 + D = x
.61x + .305x + 65 + D = x

I took total testers = 1000 because that gives me nice numbers to deal with. Also, if I use 200 total testers, that gives me A = 122, B = 61, C = 65...that's over 200 without considering D.

x = 400
A = 244, B = 122, C = 65..also over 400

x = 600
A = 366, B = 183 C = 65....also over 600

x = 800
A = 488, B = 244, C = 65...D = 3...not an option on the list.

x = 1000
A = 610 B = 305 C = 65 D = 20....the first time I get an answer that is an option in the question.

I suppose there is another way to figure this up

.61x + .305x + 65 + D = x
.915 + 65 + D = x
65 + D = 0.085x

Even if D = 0, that leaves 65 / 0.085 = x...so the minimum number of testers (with D = 0) is 764.7.

So we know the total number can't be less than that...and we've already seen 800 doesn't work...next logical step is 1000 which results in 20 and it's a possible answer.

My (usual) silly mistake, i read 65 as 65%

continuing from C+D=8.5%*T => D = 8.5%T-65
Now for D to be +ve, T>= 800

For T= 800, D= 68-65=3 (not a valid choice)
For T= 1000, D = 85-65 = 20 which is (D).

if we go furhter,
For T= 1200, D = 102-65=37 (not a valid choice)

now the Question is, what if 37 was one of the choices? Any idea what should we do?

Could you please explain how you get that the total number at least 800???

Hi earnit, the question can be solved without necessarily going into the values of T. In fact most of such PS questions can be simplified into expressions which would give you a pattern about the required values. The pattern can then be used to eliminate the option choices.

In this case, we know that C+D= 8.5% of T

We can write \(T = \frac{(65+D)*1000}{85}\).

Hence, \(T= \frac{(65+D)*200}{17}\) \(= \frac{(68+D -3)*200}{17}\). Since 68 is a multiple of 17, for T to be an integer, (D -3 ) has to be a multiple of 17. So D has to be 3 greater than any multiple of 17. Only option which satisfies this condition is 20

Hope this helps!

Regards
Harsh

I hope in the expression it must be 8.5 not 85..

T=(65+D)∗100/85

Because if C+D=8.5% of T
then, C+D=8.5*T/100
Thus T=(65+D)∗100/8.5
But even here the multiple of 17 for 68 follows..
Please help if I am wrong..

Hi Bunuel,

I am getting C+ d = 8.5 % of total

As A = 61%
B= 30.5 %


so c+ d = 8.5% T.

But I got stuck here.

Could you please provide your comments on this.

Regards

Hi there!

C + D = 8.5% of X (X=total number) . Given C = 65

After substituting and rearranging , we get :

D= (85/1000)X - 65.

Now, problem solving is all about getting the answer with minimum calculation. Options always play a significant role in this aspect.

If we carefully look into the options, we will figure that considering X=1000, we will get D=20. (Considering anyother value of X doesnt suffice any option).

Take away: Options are an important tool for reasoning and getting the correct answer. Keep an eye to this fact.

I set up an equation and plugged in the answers. I set the total as "T".
A=0.61T
B=30.5T
C=65
D= 20(plugged in from answer choice)

91.5T+85=100T
85=8.5T
T=1 or 100%

agree with what was said above
solved the same way...
61+30.5 = 91.5%
rest = 8.5%
total people x
85x/1000 = 65+D
x = (65+D)*1000/85
only 20 works.

Can anyone please tell why are we taking B = 1/2 A? If 61.5 % of the people preferred A then isnt it possible than there are people who also prefer brand B in this 61.5%?

Thanks in advance

I think the trick is in the way it is worded.

61% preferred brand A and exactly half as many preferred brand B.

No, matter what 61.5% signifies, half of that number was opted by B. Half of that number translates to half the percentage. Hope its clear.

All customers who participated told the organizer which variety they thought was the most similar to freshly-squeezed orange juice.

The above implies that each participant chose exactly one variety of juice, the one he/she thought was the most similar to freshly-squeezed orange juice.

Let total = 1000
A+B = 91.5% = 915
C = 65
D = 20
Total 1000