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21 Feb 2016, 22:08
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Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
75%
(hard)
Question Stats:
53% (02:27) correct
47%
(02:03)
wrong
based on 117
sessions
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Time
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Not Attempted Yet
Let set A={all the integer between 1 and k inclusively such that k is less than 50}. If m is ‘0s’ number A and n is ‘4s’ number in set A, n=?
1) n>m
2) n=m+11
* A solution will be posted in two days.
1) n>m
2) n=m+11
* A solution will be posted in two days.
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22 Feb 2016, 03:19
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MathRevolution
Hi all,
Seems there are a few typing errors, but in all probability the Q means
I feel the Qs tells us that m is the number of times digit 0 is used in set A , and n is the number of times digit 4 is used in set A ..
INFERENCE:-
every 10 numbers till 30 -- 1 to 10 ; 11 to 20 ; 20 to 30 will have same number of m and n..
lets see the choices..
1) n>m
n>m.. n will always be equal to or greater than m.
insuff
2) n=m+11
till 30 we have equal number of 4 and 0 used..
the next two numbers are 34 and 40.. one 4 is extra..
the numbers hereafter will keep increasing only 4..
so till 49- 1*8+2*1= 10 extra 4s.. all numbers from 41 to 49 will have a single 4 apart from 44, where there will be 2 4s..
so till 49 there are 11 extra 4s.. or n=m+11..
Suff
23 Feb 2016, 18:39
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Forget conventional ways of solving math questions. In DS, Variable approach is the easiest and quickest way to find the answer without actually solving the problem. Remember equal number of variables and independent equations ensures a solution.
Let set A={all the integer between 1 and k inclusively such that k is less than 50}. If m is ‘0s’ number A and n is ‘4s’ number in set A, n=?
1) n>m
2) n=m+11
In the original condition, there are 2 variables(m,n), which should match with the number of equations. So you need 2 equations. For 1) 1 equation for 2) 1 equation, which is likely to make C the answer.
When 1) & 2), just only for 2), n>m is valid and k=49 when substituting, which makes m=4, n=15. Thus, it is unique and sufficient. Then, the answer is B. This kind of integer question, one of the key questions, is a very critical question, which can lead you to score 50-51.
Therefore, the answer is B.
For cases where we need 2 more equations, such as original conditions with “2 variables”, or “3 variables and 1 equation”, or “4 variables and 2 equations”, we have 1 equation each in both 1) and 2). Therefore, there is 70% chance that C is the answer, while E has 25% chance. These two are the majority. In case of common mistake type 3,4, the answer may be from A, B or D but there is only 5% chance. Since C is most likely to be the answer using 1) and 2) separately according to DS definition (It saves us time). Obviously there may be cases where the answer is A, B, D or E.
Let set A={all the integer between 1 and k inclusively such that k is less than 50}. If m is ‘0s’ number A and n is ‘4s’ number in set A, n=?
1) n>m
2) n=m+11
In the original condition, there are 2 variables(m,n), which should match with the number of equations. So you need 2 equations. For 1) 1 equation for 2) 1 equation, which is likely to make C the answer.
When 1) & 2), just only for 2), n>m is valid and k=49 when substituting, which makes m=4, n=15. Thus, it is unique and sufficient. Then, the answer is B. This kind of integer question, one of the key questions, is a very critical question, which can lead you to score 50-51.
Therefore, the answer is B.
For cases where we need 2 more equations, such as original conditions with “2 variables”, or “3 variables and 1 equation”, or “4 variables and 2 equations”, we have 1 equation each in both 1) and 2). Therefore, there is 70% chance that C is the answer, while E has 25% chance. These two are the majority. In case of common mistake type 3,4, the answer may be from A, B or D but there is only 5% chance. Since C is most likely to be the answer using 1) and 2) separately according to DS definition (It saves us time). Obviously there may be cases where the answer is A, B, D or E.
