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07 Nov 2019, 03:17
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E
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If a and b are non-zero single digit integers such that \(a^b = 1\), what is the value of b?
(1) \(−1 ≤ b^a ≤ 1\)
(2) \(10a + b\) raised to any positive power always has its units digit as b.
Are You Up For the Challenge: 700 Level Questions
(1) \(−1 ≤ b^a ≤ 1\)
(2) \(10a + b\) raised to any positive power always has its units digit as b.
Are You Up For the Challenge: 700 Level Questions
26 Nov 2019, 05:52
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@kitipriyanka,i am no expert but I could help
If a and b are non-zero single digit integers such that a^b=1 what is the value of b?
(1) −1≤b^a≤1
(2) 10a+b10a+b raised to any positive power always has its units digit as b.
Before we answer the question , what non zero integers will give us a^b =1.
Either 1 raised to the power any integer or -1 raised to an even integer
Statement 1 : a=1,b=1 works for us.a=-1 and b=6 works as well.Insufficient
statement 2 : Now we are told in the stem that, a and b are non zero digits. Meaning 10a+b will have its units digit as b.We know that numbers with the base of 0,1,5 or 6 when raised to a positive power will retain the units digit of the base.Obviously,b can not be 0 but it can be 1 or 5 or 6.In sufficient
together if b=6 and a =-1 ,we satisfy both statements and the question stem.If b=1 and a=1,we satisfy both statements and the question stem as well.In both cases b has 2 different values of 1 and 6.Insufficient
Answer is E
If a and b are non-zero single digit integers such that a^b=1 what is the value of b?
(1) −1≤b^a≤1
(2) 10a+b10a+b raised to any positive power always has its units digit as b.
Before we answer the question , what non zero integers will give us a^b =1.
Either 1 raised to the power any integer or -1 raised to an even integer
Statement 1 : a=1,b=1 works for us.a=-1 and b=6 works as well.Insufficient
statement 2 : Now we are told in the stem that, a and b are non zero digits. Meaning 10a+b will have its units digit as b.We know that numbers with the base of 0,1,5 or 6 when raised to a positive power will retain the units digit of the base.Obviously,b can not be 0 but it can be 1 or 5 or 6.In sufficient
together if b=6 and a =-1 ,we satisfy both statements and the question stem.If b=1 and a=1,we satisfy both statements and the question stem as well.In both cases b has 2 different values of 1 and 6.Insufficient
Answer is E
General Discussion
07 Nov 2019, 11:57
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from the given,
if a= 1, then b = any integer from -9 to 9 except 0
if a = -1, then b = any even integer from -8 to 8 except 0
from statement (1),
if a =1, then b = 1 or -1
if a = -1, then b = any integer from -9 to 9 except 0 --> insufficient
from statement (2),
if a =1, then b = 1,5,6 (mono-cyclic integers) or -5 ( which leads to a mono-cyclic integer 5)
if a =-1, then b = 5 or -5 (which lead to a number with 5 as its unit digit) --> insufficient
upon combining,
if a = 1, then b = 1 --> sufficient C
if a = -1, then b has no valid common value (which means that a is not equal -1)
if a= 1, then b = any integer from -9 to 9 except 0
if a = -1, then b = any even integer from -8 to 8 except 0
from statement (1),
if a =1, then b = 1 or -1
if a = -1, then b = any integer from -9 to 9 except 0 --> insufficient
from statement (2),
if a =1, then b = 1,5,6 (mono-cyclic integers) or -5 ( which leads to a mono-cyclic integer 5)
if a =-1, then b = 5 or -5 (which lead to a number with 5 as its unit digit) --> insufficient
upon combining,
if a = 1, then b = 1 --> sufficient C
if a = -1, then b has no valid common value (which means that a is not equal -1)
