What is the sum of all the possible integral values of
xthat satisfy the following inequality?
19x − 2 ≤ (x + 4)^2 ≤ 21x − 6
OPTIONS
1) 32
2) 37
3) 36
4) 30
5) 39
@sujamait said:What is the sum of all the possible integral values ofxthat satisfy the following inequality?19x − 2 ≤ (x + 4)^2 ≤ 21x − 6OPTIONS1) 32 2) 37 3) 36 4) 30 5) 39
EDITED
32 
@sujamait said:What is the sum of all the possible integral values ofxthat satisfy the following inequality?19x − 2 ≤ (x + 4)^2 ≤ 21x − 6OPTIONS1) 32 2) 37 3) 36 4) 30 5) 39
32
2,9,10,11
2,9,10,11
@ScareCrow28 said:Sirjee... It's not necessary that 2x+y be = 0 ..If p=0 then (2x+y) need not be 0Then we only get y=-2If we put y=-2 in option (4) ..We get real values of "x"Likewise..if we put..r=0..then we only get (2x+y)=0..From there also we get real valuesSo, why not option 4?? I guess the question should have given" p, q, and r are non-zero numbers in AP" ??
p,q,r is in ap so 2q=p+r
p-2y+r=0
comapring it wid px+qy+r=0 ,we get x=1 y=-2
eqn 2 satisfy it
p.s. can be solved if we assume p,q,r to be any terms in ap...(provided lucky enuf to get only one eqn satisfying :P)
@amresh_maverick said:@sujamait x= 9+ 10+11 = 30
@deedeedudu said:322,9,10,11
the required sum is 2 + 9 + 10 + 11 = 32
@jain4444 said:"dusra" is a better word A and Bcan doa apiece of work in 40 and 50days if they worka t an alternative days with A beginning in how many days the work will be finished
44(2/5) days
@lopagargg said:p,q,r is in ap so 2q=p+r p-2y+r=0 comapring it wid px+qy+r=0 ,we get x=1 y=-2 eqn 2 satisfy it
Please read my post carefully 😃 p or r can be 0
@ScareCrow28 said:Please read my post carefully p or r can be 0
bypassed dat...thinking we need a ap or am i doing some blunder
@sujamait said:the required sum is 2 + 9 + 10 + 11 = 32
BUt what's the mthod?? how to find out that only these values find?? i could find out that 2 will satisfy.. but how to find out the rest
@lopagargg said:bypassed dat...thinking we need a ap or am i doing some blunder
No blunder..Its just that question needs to provide that p, q and r are non-zero numbers.. At least that is what i think :P
@chandrakant.k said:BUt what's the mthod?? how to find out that only these values find?? i could find out that 2 will satisfy.. but how to find out the rest
19x-2
from 1st inequality___(x-9)(x-2)>=0 __=> x>=9 or x
from 2nd inequality___(x-11)(x-2) 2
Hence x=2,9,10,11 satisfy
@chandrakant.k said:BUt what's the mthod?? how to find out that only these values find?? i could find out that 2 will satisfy.. but how to find out the rest
Given inequality is 19x − 2 ≤ (x + 4)^2 ≤ 21x − 6
Consider 19x − 2 ≤ (x + 4)^2
19x − 2 ≤ x^2 + 8x + 16
x^2 − 11x + 18 ≥ 0
(x − 2)(x − 9) ≥ 0
Hence, x ∈ (-∞, 2] ∪ [9, ∞) … (i)
Consider (x + 4)2 ≤ 21x − 6
x2 − 13x + 22 ≤ 0
(x − 2)(x − 11) ≤ 0
Hence, x ∈ [2, 11] … (ii)
From (i) and (ii), we have
x = 2 or x ∈ [9, 11]
Hence the possible values of x are 2, 9, 10 and 11.
Thus, the required sum is 2 + 9 + 10 + 11 = 32
Hence, option 1.
Consider 19x − 2 ≤ (x + 4)^2
19x − 2 ≤ x^2 + 8x + 16
x^2 − 11x + 18 ≥ 0
(x − 2)(x − 9) ≥ 0
Hence, x ∈ (-∞, 2] ∪ [9, ∞) … (i)
Consider (x + 4)2 ≤ 21x − 6
x2 − 13x + 22 ≤ 0
(x − 2)(x − 11) ≤ 0
Hence, x ∈ [2, 11] … (ii)
From (i) and (ii), we have
x = 2 or x ∈ [9, 11]
Hence the possible values of x are 2, 9, 10 and 11.
Thus, the required sum is 2 + 9 + 10 + 11 = 32
Hence, option 1.
@ScareCrow28 said:No blunder..Its just that question needs to provide that p, q and r are non-zero numbers.. At least that is what i think
i assumed that as it has to be ap...but any way we can solve this by assuming values or using general terms of ap p=a-b,q=a,r=a+b...would gv it a try
@amresh_maverick said:@Brooklyn take two eq at a time19x-2 (x+4)^2 solve them
i waas doing simultaneously :banghead:
i waas doing simultaneously
Same mistake ... Forgot completely about inequalities
Forgot completely about inequalities
When a four digit number is multiplied by N,the four digit number repeats itself to give an 8 digit number .If four digit number has all distinct digits then N is a multiple of ?
a)11 b) 37 c)73 d) 27
a)11 b) 37 c)73 d) 27