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11 Apr 2025, 00:30
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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:
35%
(medium)
Question Stats:
69% (01:21) correct
31%
(01:28)
wrong
based on 68
sessions
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There are total of 20 balls, and the balls each have a number from “1” to “6”. Does at least one of the balls have the number “1”?
(1) The number of the balls that has the same number does not exceed 4.
(2) There are more balls that have “6” than the balls that have “5”.
Source: Math Revolution
(1) The number of the balls that has the same number does not exceed 4.
(2) There are more balls that have “6” than the balls that have “5”.
Source: Math Revolution
11 Apr 2025, 00:48
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T = 20
Each can be numbered from 1-6
At least one of the balls have the number “1”?
Statement 1
Number of balls with same number doesn't exceed 4
If we don't consider 1, all the other balls if there are 4 of them, makes 20. Making the answer No
However, if we consider the balls do not have the same number, then we wil; have 1 in the mic, making the answer Yes
Insufficient
Statement 2
Balls with 6 > Balls with 5
Balls with 6 and balls with 5 could have number (2,1), (17,3), (20,0), ...
There are multiple possibilities, with no way to identify the number of balls with 1
Insufficient
Together, we know all the balls cannot be more than 4 and if Balls with 6 > Balls with 5, then possible number of balls could be
ball number 6 - 5 - 4 - 3 - 2 - 1
ball count. 4 - 3 - 4 - 4 - 4 - 1
Even if we keep all the other balls count max, we have 1 left for ball numbered 1. this makes the answer yes
Sufficient
Each can be numbered from 1-6
At least one of the balls have the number “1”?
Statement 1
Number of balls with same number doesn't exceed 4
If we don't consider 1, all the other balls if there are 4 of them, makes 20. Making the answer No
However, if we consider the balls do not have the same number, then we wil; have 1 in the mic, making the answer Yes
Insufficient
Statement 2
Balls with 6 > Balls with 5
Balls with 6 and balls with 5 could have number (2,1), (17,3), (20,0), ...
There are multiple possibilities, with no way to identify the number of balls with 1
Insufficient
Together, we know all the balls cannot be more than 4 and if Balls with 6 > Balls with 5, then possible number of balls could be
ball number 6 - 5 - 4 - 3 - 2 - 1
ball count. 4 - 3 - 4 - 4 - 4 - 1
Even if we keep all the other balls count max, we have 1 left for ball numbered 1. this makes the answer yes
Sufficient
Bunuel
11 Apr 2025, 04:44
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Answer:C Together Sufficient
statement 1: The number of the balls that has the same number does not exceed 4
say each balls from 2-6 0r 1-5 are 4 in count, then its not sufficient to guarentee that number 1 is present not sufficient
statement 2: There are more balls that have “6” than the balls that have “5”.
say count of 6=2, count 5=1 then count of ball with 3 number can be 17 as no other constraints given. hence not sufficient
lets try 1+2 statement
count 2=4,3=4,4=4,5=3,6=4 count of 5=3 because statement 2 says count of 5< count of 6. and max count of any ball is 4. hence total count is 19 in extreme case. which means atleast 1 ball is numbered 1
hence together sufficient
statement 1: The number of the balls that has the same number does not exceed 4
say each balls from 2-6 0r 1-5 are 4 in count, then its not sufficient to guarentee that number 1 is present not sufficient
statement 2: There are more balls that have “6” than the balls that have “5”.
say count of 6=2, count 5=1 then count of ball with 3 number can be 17 as no other constraints given. hence not sufficient
lets try 1+2 statement
count 2=4,3=4,4=4,5=3,6=4 count of 5=3 because statement 2 says count of 5< count of 6. and max count of any ball is 4. hence total count is 19 in extreme case. which means atleast 1 ball is numbered 1
hence together sufficient
