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07 Jul 2021, 01:30
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C
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Difficulty:
35%
(medium)
Question Stats:
67% (01:27) correct
33%
(01:27)
wrong
based on 98
sessions
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Not Attempted Yet
If a, b and c are integers, what is the value of a?
(1) 2^a + 2^b = 33
(2) ac = 5
(1) 2^a + 2^b = 33
(2) ac = 5
08 Jul 2021, 01:15
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If a, b and c are integers, what is the value of a?
(1) 2^a + 2^b = 33. Here notice that neither a nor be can be a negative integer. For example, if a is negative, then 2^a will be a fraction from 0 to 1 and the sum of a fraction and an integer or the sum of two such fractions cannot equal to 33. Thus both of them must be nonnegative integers. So, we have that 33 is equal to the sum of powers of 2. By trial and error we can get that 33 can be broken in the sum of powers of 2 only in one way: 33 = 1 + 32 = 2^0 + 2^5. This implies that a = 0 and b = 5 or vise-versa. Not sufficient.
(2) ac = 5. 5 can be broken into the product of two integers in the following ways: 5 = 1*5 = (-1)*(-5). Thus a could be 1, -1, 5, or -5. Not sufficient.
(1)+(2) Intersection of values of a is only a = 5. Sufficient.
Answer: C.
Hope it's clear.
(1) 2^a + 2^b = 33. Here notice that neither a nor be can be a negative integer. For example, if a is negative, then 2^a will be a fraction from 0 to 1 and the sum of a fraction and an integer or the sum of two such fractions cannot equal to 33. Thus both of them must be nonnegative integers. So, we have that 33 is equal to the sum of powers of 2. By trial and error we can get that 33 can be broken in the sum of powers of 2 only in one way: 33 = 1 + 32 = 2^0 + 2^5. This implies that a = 0 and b = 5 or vise-versa. Not sufficient.
(2) ac = 5. 5 can be broken into the product of two integers in the following ways: 5 = 1*5 = (-1)*(-5). Thus a could be 1, -1, 5, or -5. Not sufficient.
(1)+(2) Intersection of values of a is only a = 5. Sufficient.
Answer: C.
Hope it's clear.
General Discussion
07 Jul 2021, 03:22
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Statement (1) 2^a + 2^b = 33
From the above statement we can say
value of a and b can be (0, 5) or (5, 0)
a can be 0 or 5
Not sufficient
statement (2) ac = 5
a and c are not zero and
a can be 1 or 5
Not sufficient
Combined
a is 5
Sufficient
(C) is the answer IMO
From the above statement we can say
value of a and b can be (0, 5) or (5, 0)
a can be 0 or 5
Not sufficient
statement (2) ac = 5
a and c are not zero and
a can be 1 or 5
Not sufficient
Combined
a is 5
Sufficient
(C) is the answer IMO
Bunuel
