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If integers p and q are the roots of the equation ax^2 + bx + c = 0, w
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14 Jun 2017, 06:30
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If integers p and q are the roots of the equation ax^2 + bx + c = 0, where a, b and c are constants and a > 0, by what percentage is c greater than b? (1) p+1 = q – 3 (2) The greatest number that divides both p and q is 2 and the smallest number that is divisible by both p and q is 12
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Re: If integers p and q are the roots of the equation ax^2 + bx + c = 0, w
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14 Jun 2017, 08:29
Product of LCM and HCF of two numbers is equal to the product of the numbers Sent from my ONEPLUS A3003 using GMAT Club Forum mobile app



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Re: If integers p and q are the roots of the equation ax^2 + bx + c = 0, w
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17 Jun 2017, 15:22
@bunuel...Can u suggest the best approach, not able to understand this one
If integers p and q are the roots of the equation ax^2 + bx + c = 0, where a, b and c are constants and a > 0, by what percentage is c greater than b?
(1) p+1 = q – 3 (2) The greatest number that divides both p and q is 2 and the smallest number that is divisible by both p and q is 12



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Re: If integers p and q are the roots of the equation ax^2 + bx + c = 0, w
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17 Jun 2017, 16:14
There is a mistake in a question, it shouldn't be by what percent c is greater than b, I suppose it should be just a different or something like that, if so, the answer is C Before moving to the statements I would like to mention that p*q=c and pq = b Statement 1: Not sufficient. Can be any number. Ex: 12 and 19, 12+1=103 or let's say 5 and 1, 5+1= 13 Statement 2: Again not sufficient. From this statement, we can find the value of p*q which is GCF*LCM= 2*12=24, from here we can have the following combinations of values of P and Q: (12, 2), (12 , 2), (12, 2), (2 , 12), (4, 6), (4 ,6), (4, 6) and (6, 4) Combining this 2 statements together we can say that P and Q must be equal to (4, 6) as this is the only pair that satisfies the statement 1. 6+1=43 7=7. Now we can calculate the C and b: C=6*4=24 b=6+4=2 and b=2 C is not greater than b. However, you cannot find the percent difference between these 2 numbers as one of them is negative, while the other is positive
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Re: If integers p and q are the roots of the equation ax^2 + bx + c = 0, w
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20 Jun 2017, 09:04
Can anyone explain this problem a bit more clearly



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If integers p and q are the roots of the equation ax^2 + bx + c = 0, w
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20 Jun 2017, 10:51
We have quadratic equation ax^2 + bx + c = 0(where a, b and c are constants and a>0) We need to find out what percentage is 'c' greater than b(absolute value of b). Also known are the roots of the roots are p and q. (1) p+1 = q–3
Assume values for p and q which satisfy the equation. Example 1 : p=+2,q=+5. A quadratic equation can be formed by (xp)(xq) (x2)(x5) => x^2 7x +10 = 0. Here c(10) is around 42.85% greater than b, which is 7. Example 2 : p=+2,q=0. A quadratic equation can be formed by (xp)(xq) (x2)(x) => x^2 2x +1 = 0 Here c(1) is around 50% lesser than b, which is 2. Clearly insufficient. (2) The greatest number that divides both p and q is 2 and the smallest number that is divisible by both p and q is 12
Example 1 : p=2,q=6 A quadratic equation can be formed by (xp)(xq) (x+2)(x+6) => x^2+4x+12 Here c(12) is around 200% greater than b, which is 4. Example 2: p=4,q=6 A quadratic equation can be formed by (xp)(xq) (x+4)(x+6) => x^2+10x+24 Here c(24) is around 140% greater than b, which is 10.Clearly insufficient. When we combine both the statements, The only value possible for p & q, is p=4,q=6When p=4,q=6 the conditions in both the statements are satisfied and the quadratic equation x^2  2x  24=0 This has value of c(24) which is 1100% greater than b. Hence the combination of these statements is sufficient( Option C)
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If integers p and q are the roots of the equation ax^2 + bx + c = 0, w
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02 Jul 2017, 08:15
We know that, Sum of the roots= p+q= b/a AND Product of the roots= pq= c/a
From statement 1, p+1= q3 , i have taken 2 cases; Case1 let p=4, q=8; then b/a= 12, c/a=32 Case2 let p=5 , q= 7; then b/a= 2, c/a= 35 not sufficient as we get different answers
From statement 2, HCF of p and q =2 and LCM of p and q =12 Different combinations are possible= (12, 2), (12, 2), (12 , 2), (2 , 12), (4, 6), (4 ,6), (4, 6) and (6, 4) not sufficient as we get different answers
Combining both statements, out of the different combinations in statement 2, only two values satisfy case1 p=6, q=4 ; p+1= q3; 6+1= 43; 7=7 so p+q= 64=2= b/a and pq= 6 * 4= 24= c/a
case2 p=4, q=6 ; p+1= q3; 4+1= 63; 3=3 so p+q= 4+6=2= b/a and pq= 4 * 6= 24= c/a
from both the cases, we can deduce that; b=2a; b= 2a and c=24a as a>0, so b= positive but c is negative ideally, we will not be able to find the answer as c will not be greater than b but according to me, we can write (cb) * 100/b (24a+2a) * 100/ 2a= 1100% i.e. c is greater than b by 1100%.
So answer= C
Please let me know if i am wrong?



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Re: If integers p and q are the roots of the equation ax^2 + bx + c = 0, w
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08 Nov 2018, 02:10
GMATinsight Can you share an easier explanation to this question?



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Re: If integers p and q are the roots of the equation ax^2 + bx + c = 0, w
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08 Nov 2018, 03:11
s111 wrote: GMATinsight Can you share an easier explanation to this question? s111 Here is my way of solving this question Quote: If integers p and q are the roots of the equation ax^2 + bx + c = 0, where a, b and c are constants and a > 0, by what percentage is c greater than b?
(1) p+1 = q – 3 (2) The greatest number that divides both p and q is 2 and the smallest number that is divisible by both p and q is 12 Question REPHRASED: We need to know the sign and value of c and the absolute value of b to answer the questionStatement 1: p+1 = q – 3multiple solutions are possible hence NOT SUFFICIENT Statement 2: The greatest number that divides both p and q is 2 and the smallest number that is divisible by both p and q is 12i.e. HCF of p and q = 2 and LCM of p and q = 12 Property: Product of two numbers = Product of their LCM and HCF i.e. p * q = 2*12 = 24 Product of factors of any quadratic equation ax^2 + bx + c = 0 is given by c/a i.e. product of roots here = +24 or 24 (as signs of p and q are still unknown) still no information about b hence NOT SUFFICIENT Combining the two statementsWe have p+1 = q – 3 and p * q = 24 24 may be written in following ways (i.e. values of p and q may be as follows in any order) 1*24 but this pair of values does NOT satisfy p+1 = q – 3 2*12 but this pair of values do NOT satisfy p+1 = q – 3 3*8 but this pair of values do NOT satisfy p+1 = q – 3 4*6 this satisfies if p = 6 and q = 4 i.e. roots of the equation are 6 and 4 i.e. \(ax^2 + bx + c = (x6)*(x+4)\) i.e. \(ax^2 + bx + c = x^2  2x  24\) i.e. a = 1, b = 2 and c = 24 now we can calculate with CERTAINTY the percentage required hence SUFFICIENT Answer: Option C
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Re: If integers p and q are the roots of the equation ax^2 + bx + c = 0, w &nbs
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