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23 Jun 2020, 03:59
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E
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:
57% (02:14) correct
43%
(02:07)
wrong
based on 192
sessions
History
Date
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If a, b, c, and d are non-negative integers and \(a(2^3)+b(2^2)+c(2^1)+d(2^0)=17\), which of the following could be the product of \(abcd\) ?
I. 0
II. 2
III. 3
A. I only
B. II only
C. I and II only
D. II and III only
E. I, II, and III
I. 0
II. 2
III. 3
A. I only
B. II only
C. I and II only
D. II and III only
E. I, II, and III
23 Jun 2020, 04:06
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8a + 4b + 2c + d = 17
Case 1: a = 2, b = 0 , c = 0, d = 1
=> abcd = 0
Case 2: abcd = 2
=> One of them is 2 and all others are 1
The values are:
a = 1, b = 1, c = 2, d = 1
Case 3: abcd = 3
=> One of them is 3, and all others are 1.
Possible values: a = 1, b = 1, c = 1, d = 3
=> All statements could be true.
=> Answer: E
Posted from my mobile device
Case 1: a = 2, b = 0 , c = 0, d = 1
=> abcd = 0
Case 2: abcd = 2
=> One of them is 2 and all others are 1
The values are:
a = 1, b = 1, c = 2, d = 1
Case 3: abcd = 3
=> One of them is 3, and all others are 1.
Possible values: a = 1, b = 1, c = 1, d = 3
=> All statements could be true.
=> Answer: E
Posted from my mobile device
23 Jun 2020, 04:11
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Bunuel
If a, b, c, and d are non-negative integers and \(a(2^3)+b(2^2)+c(2^1)+d(2^0)=17\), which of the following could be the product of \(abcd\) ?
I. 0
II. 2
III. 3
A. I only
B. II only
C. I and II only
D. II and III only
E. I, II, and III
I. 0
II. 2
III. 3
A. I only
B. II only
C. I and II only
D. II and III only
E. I, II, and III
First of all, Non-Negative Integer Includes Zero
(Zero is neither positive, nor negative)
We have a(8) + b(4) + c(2) + d(1) = 17
suppose a=b=c=1; we'll have 8 + 4 + 2 + d = 17
therefore d = 3
Product = 3
Suppose a = b = 1 and c = 2
8 + 4 + 2*2 + d = 17
We'll have d = 1
Product = 2
Suppose a = b = c = 0 "(given: Non-Negative ) and d = 17
We'll have product = 0
Therefore, answer = (E)
