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If  -7 <= p <= 9 and -8<=q<= 6, then each of the following must

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devashish2407
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If  -7 <= p <= 9 and -8<=q<= 6, then each of the following must [#permalink] New post   26 Mar 2024, 08:39
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If \(-7 \leq {p} \leq {9} \) and \(-8 \leq {q} \leq {6}\), then each of the following must be true EXCEPT:

A. \(p + q\leq{15}\)
B. \(p - q\leq{17}\)
C. \(pq \leq 72\)
D. \( p + q \geq -15\)
E. \(pq \geq -56\)
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Bunuel
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If  -7 <= p <= 9 and -8<=q<= 6, then each of the following must [#permalink] New post   26 Mar 2024, 08:56
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If \(-7 \leq {p} \leq {9} \) and \(-8 \leq {q} \leq {6}\), then each of the following must be true EXCEPT:

A. \(p + q\leq{15}\)
B. \(p - q\leq{17}\)
C. \(pq \leq 72\)
D. \( p + q \geq -15\)
E. \(pq \geq -56\)
­
A. \(p + q\leq{15}\)

The greatest sum is obtained when p is 9 and q is 6. In this case, p + q = 15. Hence, this option must be true.

B. \(p - q\leq{17}\)

The greatest difference is obtained when p is 9 and q is -8. In this case, p - q = 17. Hence, this option must be true.

C. \(pq \leq 72\)

The greatest product is obtained when p = -7 and q = -8. In this case, pq = 56. Hence, this option must be true.

D. \( p + q \geq -15\)

The smallest sum is obtained when p = -7 and q = -8. In this case, p + q = -15. Hence, this option must be true.

E. \(pq \geq -56\)

The smallest product is obtained when p = 9 and q = -8. In this case, pq = -72. Hence, this option is NOT always be true.

Answer: E.
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Re: If  -7 <= p <= 9 and -8<=q<= 6, then each of the following must [#permalink] New post   27 Mar 2024, 18:52
devashish2407 wrote:
If \(-7 \leq {p} \leq {9} \) and \(-8 \leq {q} \leq {6}\), then each of the following must be true EXCEPT:

A. \(p + q\leq{15}\)
B. \(p - q\leq{17}\)
C. \(pq \leq 72\)
D. \( p + q \geq -15\)
E. \(pq \geq -56\)

­In this type of questions we need to start with POE, 

p+q ka max value will be 15, Hence p+q will always be less than or equal to 15

Similarly we can do for other options. 

pq Is always >-56, 
To know the least value of this p max q min(-ve)m or p min(-ve) q max, -56, -72. 

Hence E is not always true there exists a value of pq which is less than -56;

IMO E
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Re: If  -7 <= p <= 9 and -8<=q<= 6, then each of the following must [#permalink] New post   28 Mar 2024, 03:51
@devashish2407Asked: If \(-7 \leq {p} \leq {9} \) and \(-8 \leq {q} \leq {6}\), then each of the following must be true EXCEPT:

\(-7 \leq {p} \leq {9} \)
\(-8 \leq {q} \leq {6}\)
\(-15 \leq {p + q} \leq 15\)

\(-7 \leq {p} \leq {9} \)
\(-6 \leq {-q} \leq {8}\)
\(-13 \leq {p - q} \leq 17\)

\(-72 \leq {pq} \leq 56\)

A. \(p + q\leq{15}\) : MUST BE TRUE
B. \(p - q\leq{17}\) : MUST BE TRUE
C. \(pq \leq 56 \leq 72\) : MUST BE TRUE 
D. \( p + q \geq -15\) : MUST BE TRUE
E. \(pq \geq -56\) : MAY NOT BE TRUE

IMO E
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Re: If  -7 <= p <= 9 and -8<=q<= 6, then each of the following must [#permalink]
28 Mar 2024, 03:51
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