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29 May 2023, 23:41
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C
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For any integers a, b, and c, hi(a, b, c) and lo(a, b, c) respectively denote the greatest and least values among a, b, and c. For example, hi(3, 7, 5) = 7 and lo(5, 7, 3) = 3. For integers m and n, what is the value of hi(30, m, n) ?
(1) n^2 = lo(20, n^2, p)
(2) m^2 = lo(20, m, n^3 – 4)
(1) n^2 = lo(20, n^2, p)
(2) m^2 = lo(20, m, n^3 – 4)
30 May 2023, 01:17
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Raisakatyal
Given
- hi(a, b, c) = highest value among a, b and c.
- lo(a, b, c) = lowest value among a, b and c.
Question
hi(30, m, n) = ?
Hence, we want to find whether m and n are greater than 30 and if so, between m and n which has greater value.
Statement 1
(1) \(n^2\) = lo(\(20\), \(n^2\), \(p\))
Inference: \(n^2\) is less than 20, hence
\( n = {-4,-3,-2,1,0,1,2,3,4}\)
So we can be sure that n is not greater than 30, however, we do not know whether m is greater than 30. Hence, this statement alone is not sufficient.
Statement 2
(2) \(m^2\) = lo(\(20\), \(m\), \(n^3 – 4\))
Inference:
- \(m^2 < 20\) → \( m = {-4,-3,-2,1,0,1,2,3,4}\)
- \(m^2 \leq m\) → \( 0 \leq m \leq 1\) → \( m = {0,1}\) (Note, \(m^2\) cannot be less than 'm' as 'm' is an integer)
- \(n^3 – 4 \geq 20 \) → \(n^3 \geq 24 \) → \(n \geq 2.XX \) → \( n = {3,4,5....}\)
This statement doesn't tell us whether 'n' is greater than 30. Hence, this statement alone is not sufficient.
Combined
From statement 2, we know \( m = {-4,-3,-2,1,0,1,2,3,4}\)
From statements 1 and 2, we know that \( n = {3,4}\)
As both m and n are less than 30 hi(30, m, n) = 30.
The statements combined are sufficient.
Option C
arkaja11
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Schools: ISB '27 (A) INSEAD '26 Tuck '27
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13 Jun 2024, 14:13
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Didn't understand how in statement 2 has the inference \(n^{3} - 4 > 20 \) been drawn?
Also, how can "m" even take negative values? The statement 2 cannot have LHS = positive and RHS = negative.
According to me, statement 2 will just yield 2 values of \(m = 0,1\).
But since n can take as many values, statement 2 will be insufficient.
Also, how can "m" even take negative values? The statement 2 cannot have LHS = positive and RHS = negative.
According to me, statement 2 will just yield 2 values of \(m = 0,1\).
But since n can take as many values, statement 2 will be insufficient.
