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05 Jun 2020, 08:16
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Difficulty:
65%
(hard)
Question Stats:
62% (02:31) correct
38%
(02:44)
wrong
based on 146
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A tea company sells two brands of tea leaves, Brand A and Brand B. Both the brands of tea leaves consist of three types of tea leaves, types-I, II and III, but in different weights. The cost of a kilogram of a brand of tea leaves is given by the expression $(100p+80q+50r), where p, q and r are the weights of type-I, II and III tea leaves respectively in 1 kilogram of that brand of tea leaves. Which of the two brands of tea leaves costs more?
(1) The individual percentage weights of type-I and type-III tea leaves are greater in Brand A than in Brand B
(2) The percentage weight of type-I tea leaves in Brands A and B is 40 percent and 20 percent respectively
Are You Up For the Challenge: 700 Level Questions
(1) The individual percentage weights of type-I and type-III tea leaves are greater in Brand A than in Brand B
(2) The percentage weight of type-I tea leaves in Brands A and B is 40 percent and 20 percent respectively
Are You Up For the Challenge: 700 Level Questions
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05 Jun 2020, 09:57
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IMO E
Cost expression $(100p+80q+50r)
(We need values of all PQR to determine cost of Tea Brand A and B)
Statement 1: The individual percentage weights of type-I and type-III tea leaves are greater in Brand A than in Brand B (no information regarding Type 2 tea leaves in either of the brand) (not sufficient)
Statement 2: The percentage weight of type-I tea leaves in Brands A and B is 40 percent and 20 percent respectively
(Type 2 & Type 3 both leaves information is missing)
Statement 1&2: No constraint mentioned regarding Type 2 Tea leaves it can be More in Brand B which can tame down the cost level of brand A, (Cost Can't be determined)
Posted from my mobile device
Cost expression $(100p+80q+50r)
(We need values of all PQR to determine cost of Tea Brand A and B)
Statement 1: The individual percentage weights of type-I and type-III tea leaves are greater in Brand A than in Brand B (no information regarding Type 2 tea leaves in either of the brand) (not sufficient)
Statement 2: The percentage weight of type-I tea leaves in Brands A and B is 40 percent and 20 percent respectively
(Type 2 & Type 3 both leaves information is missing)
Statement 1&2: No constraint mentioned regarding Type 2 Tea leaves it can be More in Brand B which can tame down the cost level of brand A, (Cost Can't be determined)
Posted from my mobile device
06 Apr 2025, 19:52
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The blended price of a mix per kg can be rewritten as (100q+80p+50r)/1000 = 0.1q+0.08p+0.05r, assuming q, p, r are all measured in grams. For simplicity of calculation, we can use the blended price per 1000kg which is the same as the original formula 100q+80p+50r.
Statement 1:
The price of the mixture of type I & III would be anything between 50 (where type I barely exists) and 100 (where type III barely exists). Without information about type II, we can only know that the overall mix price is also between 50 and 100 but the more there is type II, the closer it will be to 80. No definitive comparison can be drawn between A & B.
INSUFFICIENT.
Statement 2:
Knowing type I is 40% and 20% in A and B, respectively, we can write the overall mix price as:
A: 100*40%+80*(100%-40%-type III% in A)+50*(type III% in A)
B: 100*20%+80*(100%-20%-type III% in B)+50*(type III% in B)
A-B gives (40+48-30*type III% in A)-(20+64-30*type III% in B) = 4+30*(B_III% - A_III%). Since we don't know the relationship between B_III% - A_III%, the end outcome could be either positive or negative.
To illustrate, for A-B<0 (i.e. B is more expensive), 4+30*(B_III% - A_III%)<0 >> B_III% - A_III%<-13%; for A-B=0, B_III% - A_III%=-13%; for A-B>0, B_III% - A_III%>-13%. That is, given there is already proportionally more costlier type I leaves in A, there needs to be materially less type III in the mix for B to become more expensive overall than A, vice versa, with a breakeven threshold of 13% less.
INSUFFICIENT.
Combining both statements, we know A_I% is definitely greater than B_I%, and that A_III% is greater than B_III%. We can only conclude A & B's relationship based on the size of the percentage difference of type III leaves, according to the threshold identified as part of our analysis of Statement 2.
INSUFFICIENT.
Statement 1:
The price of the mixture of type I & III would be anything between 50 (where type I barely exists) and 100 (where type III barely exists). Without information about type II, we can only know that the overall mix price is also between 50 and 100 but the more there is type II, the closer it will be to 80. No definitive comparison can be drawn between A & B.
INSUFFICIENT.
Statement 2:
Knowing type I is 40% and 20% in A and B, respectively, we can write the overall mix price as:
A: 100*40%+80*(100%-40%-type III% in A)+50*(type III% in A)
B: 100*20%+80*(100%-20%-type III% in B)+50*(type III% in B)
A-B gives (40+48-30*type III% in A)-(20+64-30*type III% in B) = 4+30*(B_III% - A_III%). Since we don't know the relationship between B_III% - A_III%, the end outcome could be either positive or negative.
To illustrate, for A-B<0 (i.e. B is more expensive), 4+30*(B_III% - A_III%)<0 >> B_III% - A_III%<-13%; for A-B=0, B_III% - A_III%=-13%; for A-B>0, B_III% - A_III%>-13%. That is, given there is already proportionally more costlier type I leaves in A, there needs to be materially less type III in the mix for B to become more expensive overall than A, vice versa, with a breakeven threshold of 13% less.
INSUFFICIENT.
Combining both statements, we know A_I% is definitely greater than B_I%, and that A_III% is greater than B_III%. We can only conclude A & B's relationship based on the size of the percentage difference of type III leaves, according to the threshold identified as part of our analysis of Statement 2.
INSUFFICIENT.
