GMAT Exam > GMAT Questions > If |p-5| =3 and |q-3| = 5, which of the follo...
Start Learning for Free
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
Correct answer is option 'E'. Can you explain this answer?
Verified Answer
If |p-5| =3 and |q-3| = 5, which of the following statements must be t...
Given
- |p – 5| = 3
- |q – 3| = 5
To Find: The options that must be true(for all values of p and q)
Approach
- Since we are given expressions in p and q, we will find the possible values of p and q and then evaluate each of the expression in the options given for their trueness.
- Since, we need to look for must be true statements, any case that makes the expression in the option false will rule out the option.
Working Out
1. As | p – 5| = 3, value of p will be 3 units from away from 5 on the number line. So, following can be values of p:
- p = 5 + 3 = 8 or
- p = 5 – 3 = 2
- So, p = { 2, 8}……….(1)
2. As | q – 3| = 5, value of q will be 5 units away from 3 on the number line. So, following can be values of q:
- q = 3 + 5 = 8 or
- q = 3 – 5 = -2
- So, q = {-2, 8}………(2)
3. Evaluating Options
- p + q > 0 → As p + q = 0, when p = 2 and q = -2, this statement is not always true.
- pq ≥ 0→ Both the possible values of p are positive. For value of q = -2, the value of pq < 0. Hence this statement is not always true
- |p| = |q|→ This statement is not always true, as |p| can be 2 when |q| = 8 or vice versa.
- |p| ≥ |q|→ This statement is not always true, as |p| can be 2 when |q| = 8, in which case we will have |p| < |q|
- -6 ≤ p-q ≤ 10→ We need to find the minimum and maximum value of p – q
- Minimum( p –q) = Minimum p – Maximum q = 2 – 8 = -6
- Maximum(p – q) = Maximum p – Minimum q = 8 – (-2) = 10
- So, value of p –q would always lie between -6 and 10, inclusive. Hence, this statement is always true.
Answer: E
Most Upvoted Answer
If |p-5| =3 and |q-3| = 5, which of the following statements must be t...
Understanding the Absolute Value Equations
To solve the equations |p-5| = 3 and |q-3| = 5, we need to determine the possible values for p and q.
Finding p
- The equation |p-5| = 3 implies two scenarios:
- p - 5 = 3 → p = 8
- p - 5 = -3 → p = 2
Thus, p can be 8 or 2.
Finding q
- The equation |q-3| = 5 also implies two scenarios:
- q - 3 = 5 → q = 8
- q - 3 = -5 → q = -2
Thus, q can be 8 or -2.
Analyzing the Statements
Now we evaluate the given options:
- a) p + q 0: Not necessarily true, since p can be 2 or 8 and q can be -2 or 8.
- b) pq 0: Not necessarily true. For example, if p = 2 and q = -2, pq = -4 which is less than 0.
- c) |p| = |q|: Not true in all cases. For example, if p = 8 and q = -2, |p| does not equal |q|.
- d) |p| |q|: Not necessarily true. For example, |p| could be greater or lesser than |q| depending on the combination of their values.
- e) -6 < p="" -="" q="" />< 10:="" let's="" evaluate="" this:="" -="" if="" p="8" and="" q="8," then="" p="" -="" q="0," which="" satisfies="" the="" inequality.="" -="" if="" p="2" and="" q="-2," then="" p="" -="" q="4," which="" also="" satisfies="" the="" inequality.="" -="" if="" p="8" and="" q="-2," then="" p="" -="" q="10," which="" is="" at="" the="" upper="" limit="" but="" still="" satisfies="" the="" condition.="" thus,="" -6="" />< p="" -="" q="" />< 10="" holds="" true="" for="" all="" possible="" values="" of="" p="" and="" q.="" />Conclusion
The correct answer is option 'E': -6 < p="" -="" q="" />< 10.="" />
To solve the equations |p-5| = 3 and |q-3| = 5, we need to determine the possible values for p and q.
Finding p
- The equation |p-5| = 3 implies two scenarios:
- p - 5 = 3 → p = 8
- p - 5 = -3 → p = 2
Thus, p can be 8 or 2.
Finding q
- The equation |q-3| = 5 also implies two scenarios:
- q - 3 = 5 → q = 8
- q - 3 = -5 → q = -2
Thus, q can be 8 or -2.
Analyzing the Statements
Now we evaluate the given options:
- a) p + q 0: Not necessarily true, since p can be 2 or 8 and q can be -2 or 8.
- b) pq 0: Not necessarily true. For example, if p = 2 and q = -2, pq = -4 which is less than 0.
- c) |p| = |q|: Not true in all cases. For example, if p = 8 and q = -2, |p| does not equal |q|.
- d) |p| |q|: Not necessarily true. For example, |p| could be greater or lesser than |q| depending on the combination of their values.
- e) -6 < p="" -="" q="" />< 10:="" let's="" evaluate="" this:="" -="" if="" p="8" and="" q="8," then="" p="" -="" q="0," which="" satisfies="" the="" inequality.="" -="" if="" p="2" and="" q="-2," then="" p="" -="" q="4," which="" also="" satisfies="" the="" inequality.="" -="" if="" p="8" and="" q="-2," then="" p="" -="" q="10," which="" is="" at="" the="" upper="" limit="" but="" still="" satisfies="" the="" condition.="" thus,="" -6="" />< p="" -="" q="" />< 10="" holds="" true="" for="" all="" possible="" values="" of="" p="" and="" q.="" />Conclusion
The correct answer is option 'E': -6 < p="" -="" q="" />< 10.="" />
|
Explore Courses for GMAT exam
|
|
Top Courses for GMATView all
Question Description
If |p-5| =3 and |q-3| = 5, which of the following statements must be true?a)p + q > 0b)pq ≥ 0c)|p| = |q|d)|p| ≥ |q|e)-6 ≤ p-q ≤ 10Correct answer is option 'E'. Can you explain this answer? for GMAT 2025 is part of GMAT preparation. The Question and answers have been prepared according to the GMAT exam syllabus. Information about If |p-5| =3 and |q-3| = 5, which of the following statements must be true?a)p + q > 0b)pq ≥ 0c)|p| = |q|d)|p| ≥ |q|e)-6 ≤ p-q ≤ 10Correct answer is option 'E'. Can you explain this answer? covers all topics & solutions for GMAT 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If |p-5| =3 and |q-3| = 5, which of the following statements must be true?a)p + q > 0b)pq ≥ 0c)|p| = |q|d)|p| ≥ |q|e)-6 ≤ p-q ≤ 10Correct answer is option 'E'. Can you explain this answer?.
If |p-5| =3 and |q-3| = 5, which of the following statements must be true?a)p + q > 0b)pq ≥ 0c)|p| = |q|d)|p| ≥ |q|e)-6 ≤ p-q ≤ 10Correct answer is option 'E'. Can you explain this answer? for GMAT 2025 is part of GMAT preparation. The Question and answers have been prepared according to the GMAT exam syllabus. Information about If |p-5| =3 and |q-3| = 5, which of the following statements must be true?a)p + q > 0b)pq ≥ 0c)|p| = |q|d)|p| ≥ |q|e)-6 ≤ p-q ≤ 10Correct answer is option 'E'. Can you explain this answer? covers all topics & solutions for GMAT 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If |p-5| =3 and |q-3| = 5, which of the following statements must be true?a)p + q > 0b)pq ≥ 0c)|p| = |q|d)|p| ≥ |q|e)-6 ≤ p-q ≤ 10Correct answer is option 'E'. Can you explain this answer?.
Solutions for If |p-5| =3 and |q-3| = 5, which of the following statements must be true?a)p + q > 0b)pq ≥ 0c)|p| = |q|d)|p| ≥ |q|e)-6 ≤ p-q ≤ 10Correct answer is option 'E'. Can you explain this answer? in English & in Hindi are available as part of our courses for GMAT.
Download more important topics, notes, lectures and mock test series for GMAT Exam by signing up for free.
Here you can find the meaning of If |p-5| =3 and |q-3| = 5, which of the following statements must be true?a)p + q > 0b)pq ≥ 0c)|p| = |q|d)|p| ≥ |q|e)-6 ≤ p-q ≤ 10Correct answer is option 'E'. Can you explain this answer? defined & explained in the simplest way possible. Besides giving the explanation of
If |p-5| =3 and |q-3| = 5, which of the following statements must be true?a)p + q > 0b)pq ≥ 0c)|p| = |q|d)|p| ≥ |q|e)-6 ≤ p-q ≤ 10Correct answer is option 'E'. Can you explain this answer?, a detailed solution for If |p-5| =3 and |q-3| = 5, which of the following statements must be true?a)p + q > 0b)pq ≥ 0c)|p| = |q|d)|p| ≥ |q|e)-6 ≤ p-q ≤ 10Correct answer is option 'E'. Can you explain this answer? has been provided alongside types of If |p-5| =3 and |q-3| = 5, which of the following statements must be true?a)p + q > 0b)pq ≥ 0c)|p| = |q|d)|p| ≥ |q|e)-6 ≤ p-q ≤ 10Correct answer is option 'E'. Can you explain this answer? theory, EduRev gives you an
ample number of questions to practice If |p-5| =3 and |q-3| = 5, which of the following statements must be true?a)p + q > 0b)pq ≥ 0c)|p| = |q|d)|p| ≥ |q|e)-6 ≤ p-q ≤ 10Correct answer is option 'E'. Can you explain this answer? tests, examples and also practice GMAT tests.
|
|
Explore Courses for GMAT exam
|
|
Signup for Free!
Signup to see your scores go up within 7 days! Learn & Practice with 1000+ FREE Notes, Videos & Tests.
|
© EduRev
|
Education Revolution
|
|
Signup on EduRev and stay on top of your study goals
10M+ students crushing their study goals daily