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Difficulty:
25%
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68% (01:06) correct
32%
(01:16)
wrong
based on 53
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The symbol ⊗ represents one of the following operations: addition, subtraction, multiplication, or division. What is the value of 7⊗4?
(1) 4⊗7 < 1
(2) 4⊗3 > 1
(1) 4⊗7 < 1
(2) 4⊗3 > 1
26 Aug 2022, 22:42
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The symbol ⊗ represents one of the following operations: addition, subtraction, multiplication, or division. What is the value of 7⊗4?
(1) 4⊗7 < 1
(2) 4⊗3 > 1
(1) 4⊗7 < 1
(2) 4⊗3 > 1
Solution:
Pre-Analysis:
If ⊗ is addition, then \(7⊗4=11\)
If ⊗ is subtraction, then \(7⊗4=3\)
If ⊗ is multiplication. then \(7⊗4=28\)
If ⊗ is division, then \(7⊗4=1.75\)
Statement 1: \(4⊗7<1\)
If ⊗ is addition, then \(4⊗7=11\) ............(not \(<1\))
If ⊗ is subtraction, then \(4⊗7=-3\) ........(\(<1\))
If ⊗ is multiplication. then \(4⊗7=28\) .....(not \(<1\))
If ⊗ is division, then \(4⊗7=0.571\) .........(\(<1\))
So, according to this statement, ⊗ can be subtraction or division and the value of 7⊗4 in both cases are different
Thus, statement 1 alone is not sufficient and we can eliminate options A and D
Statement 2: \(4⊗3>1\)
If ⊗ is addition, then \(4⊗3=7\) ............(\(>1\))
If ⊗ is subtraction, then \(4⊗3=1\) ........(not \(>1\))
If ⊗ is multiplication. then \(4⊗3=12\) .....(\(>1\))
If ⊗ is division, then \(4⊗3=1.33\) .........(\(>1\))
So, according to this statement, ⊗ can be addition, multiplication or division and the value of 7⊗4 in all these cases are different
Thus, statement 2 alone is also not sufficient and we can eliminate option B
Combining:
According to statement 1, ⊗ is subtraction or division
According to statement 2, ⊗ is addition, multiplication or division
So, upon combining, we can infer that ⊗ is a division sign and \(7⊗4=1.75 \)
Hence the right answer is Option C
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