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20 May 2020, 03:11
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Difficulty:
95%
(hard)
Question Stats:
41% (02:42) correct
59%
(02:50)
wrong
based on 100
sessions
History
Date
Time
Result
Not Attempted Yet
If % denotes one of the arithmetic operations, addition, subtraction, multiplication or division, and if z is an integer, what is the value of 2z%z?
(1) 3%(2z) = −(z%1)
(2) (3z)%(z−1) = 5
Are You Up For the Challenge: 700 Level Questions
(1) 3%(2z) = −(z%1)
(2) (3z)%(z−1) = 5
Are You Up For the Challenge: 700 Level Questions
20 May 2020, 03:43
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Statement 1-
Case 1- %=+
3+2z = -z-1
3z=-4 (not and integer)
(rejected)
Case 2- %=-
3-2z = -z+1
-z=-2; z=2 (Possible)
2z%z = 2z-z =z =2
Case 3- %=*
6z = -z
z=0 (Possible)
2z%z = 2z^2 =0
Case 4- % = /
3/2z = -z
-2z^2=3 (z is not an integer)
(rejected)
2 different values of 2z%z are possible
Insufficient
Statement 2-
Case 1- %=+
\(3z+z-1 = 5\)
4z=6 (z is not an integer)
(rejected)
Case 2 %=-
\(3z-z+1 = 5\)
2z=4; z=2 (Possible)
2z%z = 2z-z =z =2
Case 3- %=*
\(3z^2-3z = 5\)
\(3^2-4*3*(-5) = 69\) is not a perfect square.
z can't be an integer
(rejected)
Case 4- % = /
\(\frac{3z}{z-1} = 5\)
3z=5z-5
2z=5; z=2.5 (rejected)
Sufficient
Case 1- %=+
3+2z = -z-1
3z=-4 (not and integer)
(rejected)
Case 2- %=-
3-2z = -z+1
-z=-2; z=2 (Possible)
2z%z = 2z-z =z =2
Case 3- %=*
6z = -z
z=0 (Possible)
2z%z = 2z^2 =0
Case 4- % = /
3/2z = -z
-2z^2=3 (z is not an integer)
(rejected)
2 different values of 2z%z are possible
Insufficient
Statement 2-
Case 1- %=+
\(3z+z-1 = 5\)
4z=6 (z is not an integer)
(rejected)
Case 2 %=-
\(3z-z+1 = 5\)
2z=4; z=2 (Possible)
2z%z = 2z-z =z =2
Case 3- %=*
\(3z^2-3z = 5\)
\(3^2-4*3*(-5) = 69\) is not a perfect square.
z can't be an integer
(rejected)
Case 4- % = /
\(\frac{3z}{z-1} = 5\)
3z=5z-5
2z=5; z=2.5 (rejected)
Sufficient
20 May 2020, 10:10
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Seriously, WHAT a brilliant question.
