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09 Jun 2020, 05:15
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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:
45%
(medium)
Question Stats:
67% (02:00) correct
33%
(01:48)
wrong
based on 689
sessions
History
Date
Time
Result
Not Attempted Yet
If \(|p-5| =3\) and \(|q-3| = 5\), which of the following statements must be true?
A. \(p + q > 0\)
B. \(pq ≥ 0\)
C. \(|p| = |q|\)
D. \(|p| ≥ |q|\)
E. \(-6 ≤ p-q ≤ 10\)
A. \(p + q > 0\)
B. \(pq ≥ 0\)
C. \(|p| = |q|\)
D. \(|p| ≥ |q|\)
E. \(-6 ≤ p-q ≤ 10\)
09 Jun 2020, 05:46
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Bunuel
\(|p-5| =3\)
i.e. p = 8 or 2
\(|q-3| = 5\)
i.e. q = 8 or -2
i.e. 0 ≤ p+q ≤ 16 Option A OUT
i.e. -16 ≤ p*q ≤ 64 Option B OUT
Option C and D are Out because lpl may be 2 and lql may be 8
i.e. -6 ≤ p-q ≤ 10
Answer: Option E
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09 Jun 2020, 07:13
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=> |P-5| = 3
=> Case 1: +P-5 = 3 => P = 8
=> Case 2: -P+5 = 3 => P = 2
=> |Q-3| = 5
=> Case 1: +Q-3 = 5 => Q = +8
=> Case 2: -Q+3 = 5 => Q = -2
Putting values in options one by one
A. P+Q > O
=> Case 1: P+Q = 8+8 > 0 (correct)
=> Case 2: p+Q = -2+2 => 0 = 0 (incorrect)
B. PQ≥0
=> Case 1: PQ = 8*8 > 0 (correct)
=> Case 2: PQ = -2*2 < 0 (incorrect)
C. |P| = |Q|
=> Case 1: |2| = |-2| = 2=2 (correct)
=> Case 2: |8| = |-2| = 8≠2 (incorrect)
D. |P| ≥ |Q|
=> Case 1: |8| ≥ |8| = (correct)
=> Case 2: |2| < |8| = (incorrect)
E. -6≤P-Q≤10
=> Case 1: P-Q = 8-(-2) = 10 (maximum value) (correct)
=> Case 2: P-Q = 2-8 = -6 (minimum value) (correct)
Answer is E
Posted from my mobile device
=> Case 1: +P-5 = 3 => P = 8
=> Case 2: -P+5 = 3 => P = 2
=> |Q-3| = 5
=> Case 1: +Q-3 = 5 => Q = +8
=> Case 2: -Q+3 = 5 => Q = -2
Putting values in options one by one
A. P+Q > O
=> Case 1: P+Q = 8+8 > 0 (correct)
=> Case 2: p+Q = -2+2 => 0 = 0 (incorrect)
B. PQ≥0
=> Case 1: PQ = 8*8 > 0 (correct)
=> Case 2: PQ = -2*2 < 0 (incorrect)
C. |P| = |Q|
=> Case 1: |2| = |-2| = 2=2 (correct)
=> Case 2: |8| = |-2| = 8≠2 (incorrect)
D. |P| ≥ |Q|
=> Case 1: |8| ≥ |8| = (correct)
=> Case 2: |2| < |8| = (incorrect)
E. -6≤P-Q≤10
=> Case 1: P-Q = 8-(-2) = 10 (maximum value) (correct)
=> Case 2: P-Q = 2-8 = -6 (minimum value) (correct)
Answer is E
Posted from my mobile device
