If -7

Question

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

Bunuel · Answer

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.

HarshaBujji · Answer

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

Kinshook · Answer

@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

Mehakgyl · Answer

For option choice (C) if the pq=72 then this wont hold true right? Since pq<= 56

Bunuel · Answer

I don't get your question. C says that  pq \leq 72 , which is always true because the greatest product is obtained when p = -7 and q = -8. In this case, pq = 56.

Spoorthii · Answer

Option C says pq is less than or 'equal to' 72. If pq is always less than 72 (in this case the greatest product is 56), how can it satisfy the condition less than or equal to? It satisfies only less than

Bunuel · Answer

"pq is less than or equal to 72" does not mean "pq" must be exactly 72; it means "pq" can be any value up to and including 72. Since the highest possible product is 56, which is less than 72, the statement holds true.

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

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