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19 Jan 2022, 07:00
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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:
85%
(hard)
Question Stats:
50% (02:35) correct
50%
(02:19)
wrong
based on 82
sessions
History
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In a survey conducted by company Q, about which tea is preferred by people, two-fifths of the surveyed people said that they preferred lemon tea while the remaining people said that they preferred ginger tea. People who preferred lemon tea were made to taste the ginger tea made by company Q. ‘x’ number of people who had preferred lemon tea initially now chose ginger tea as their preferred tea. Is x > 30?
(1) The number of people who still prefer lemon tea after tasting ginger tea made by company Q is 1/3 of the total number of people who prefer ginger tea.
(2) At most 180 people participated in the survey.
(1) The number of people who still prefer lemon tea after tasting ginger tea made by company Q is 1/3 of the total number of people who prefer ginger tea.
(2) At most 180 people participated in the survey.
30 Jan 2022, 00:38
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Bunuel
Let T be the total number of people, \(\frac{2}{5}\)T\(=\) Lemon tea, \(\frac{3}{5}\) T\(=\)Ginger tea
The stem can be denoted mathematically as :
\(\frac{2}{5}\)T \(-x = \frac{3}{5}\)T \(+ x\)
(1) The number of people who still prefer lemon tea after tasting ginger tea made by company Q is 1/3 of the total number of people who prefer ginger tea.
\(\frac{2}{5}\)T \(-x = \frac{1}{3}(\frac{3}{5}\)T \(+ x )\)
After simplification we get \(x= \frac{3}{20}\)T
Since we do not know T we cannot get the value of \(x \)
INSUFF.
(2) At most 180 people participated in the survey.
Using this info. along with what is given in the stem we get a negative value for \(x \) which is not possible therefore it means some info. is missing.
INSUFF.
\(1+2 \)
from 1 we know \(x=\frac{3}{20}\)T
From 2 we know Max. value of T \(= 180\)
So even if T is Max i.e. \(180 \) then \(x_{max} = \frac{3}{20}*180= 27 \)
Hence \(x \ngtr 30\)
SUFF.
Ans C
17 Apr 2023, 09:57
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Bunuel
Solution:
Pre Analysis:
- Initially:
- Preferred lemon tea \(=\frac{2N}{5}\)
- Preferred ginger tea \(=\frac{3N}{5}\)
- Finally:
- Preferred lemon tea \(=\frac{2N}{5}-x\)
- Preferred ginger tea \(=\frac{3N}{5}+x\)
- We are asked if x > 30 or not
Statement 1: The number of people who still prefer lemon tea after tasting ginger tea made by company Q is 1/3 of the total number of people who prefer ginger tea
- According to this statement, \(\frac{2N}{5}-x=\frac{1}{3}(\frac{3N}{5}+x)\)
\(⇒\frac{2N}{5}-x=\frac{N}{5}+\frac{x}{3}\) - This equation will give us some relation between N and x and not an exact value of x
- Thus, statement 1 alone is not sufficient and we can eliminate options A and D
Statement 2: At most 180 people participated in the survey
- According to this statement, \(N \le 180\)
- No information on x
- Thus, statement 2 alone is also not sufficient
Combining:
- From statement 1: \(\frac{2N}{5}-x=\frac{N}{5}+\frac{x}{3}\) or \(x=\frac{3N}{20}\)
- From statement 2: \(N \le 180\)
- Upon combining, we can say \(x\le \frac{3\times 180}{20}\) or \(x\le 27\)
- Clearly x is not greater than 30
Hence the right answer is Option C
