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If x is a positive integer greater than 1, what is the sum of the mult
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03 Sep 2015, 02:29
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70% (02:13) correct 30% (02:19) wrong based on 301 sessions
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If x is a positive integer greater than 1, what is the sum of the multiples of x from x to x^2, inclusive? (A) \(x(x + 1)(x1)\) (B) \(\frac{x^2(x + 1)}{2}\) (C) \(x^2(x1)\) (D) \(\frac{(x^3 + 2x)}{2}\) (E) \(x(x1)^2\) Kudos for a correct solution.
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Re: If x is a positive integer greater than 1, what is the sum of the mult
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03 Sep 2015, 04:31
goldfinchmonster wrote: Ans : B. I substituted 3 in all answer choices. Option B & C were both satisfying the condition.
So i substituted 4 instead of 3 in all answer choices, Only B option satisfied.
Can anyone tell a simpler way to solve. Algebraically: You need to find the sum : x+2x+3x+4x+5x+6x......x*(x1)+x*x = x(1+2+3+4+5+6....+x1+x) = x* (sum of numbers from 1 to x) = x* (x/2) [2*1+(x1)*1] .......(from sum of n terms of an arithmetic progression : \(S_n\) = \(\frac{n[2*a+(n1)*d]}{2}\) , where n = total number of terms, a = 1st term, d = difference between 2 consecutive terms =\(\frac{x^2(x+1)}{2}\) B is the correct answer.




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Re: If x is a positive integer greater than 1, what is the sum of the mult
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03 Sep 2015, 04:20
Ans : B. I substituted 3 in all answer choices. Option B & C were both satisfying the condition.
So i substituted 4 instead of 3 in all answer choices, Only B option satisfied.
Can anyone tell a simpler way to solve.



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Re: If x is a positive integer greater than 1, what is the sum of the mult
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03 Sep 2015, 09:53
Bunuel wrote: If x is a positive integer greater than 1, what is the sum of the multiples of x from x to x^2, inclusive?
(A) x(x + 1)(x1) (B) x^2(x + 1)/2 (C) x^2(x1) (D) (x^3 + 2x)/2 (E) x(x1)^2
Kudos for a correct solution. We have to find the sum of multiples of x from x to x^2 inclusive let x = 3 then sum of the multiples from 3 to 9 will be 3+6+9 or 3(1+2+3) let x=5 then sum of multiples from 5 to 25 will be 5+10+15+20+25 or 5(1+2+3+4+5) From these values it is clear that th sum of multiples of x from x to x^2 inclusive will be x(sum of first x natural numbers) or \(x*\) \(\frac{x(x+1)}{2}\) or \(\frac{x^2(x+1)}{2}\) Answer: B



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Re: If x is a positive integer greater than 1, what is the sum of the mult
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03 Sep 2015, 11:11
Solution:
Sum = x + 2x +3x +.. + x(x) = x(1+2+3...+x) = x((x/2)(2 +(x1)) = (x^2)(x+1)/2 So, option B



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Re: If x is a positive integer greater than 1, what is the sum of the mult
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06 Sep 2015, 05:46
Bunuel wrote: If x is a positive integer greater than 1, what is the sum of the multiples of x from x to x^2, inclusive?
(A) x(x + 1)(x1) (B) x^2(x + 1)/2 (C) x^2(x1) (D) (x^3 + 2x)/2 (E) x(x1)^2
Kudos for a correct solution. MANHATTAN GMAT OFFICIAL SOLUTION:We can approach this problem with algebra or by plugging numbers. Even though the latter’s probably faster and easier, it’s good to have both tools up your sleeve. Algebraic solution (harder):The multiples of x are x, 2x, 3x, etc. The square of x is also a multiple of x, of course—it’s just x times x, or the xth multiple of x. So the list we care about is x, 2x, 3x… up to x^2. The sum of these numbers can be written as x + 2x + 3x + … + x^2. We can now factor out an x to get x(1 + 2 + 3 + … + x). Now, the sum that remains (that is, 1 + 2 + 3 + … + x) is a sum of consecutive integers, which is evenly spaced. It’s easy to calculate the average (arithmetic mean) of an evenly spaced set: just add up the outermost numbers and divide by 2: Average of {1, 2, 3, …, x} = (x + 1)/2 The number of numbers in that set is just x, since there are x consecutive integers between 1 and x, inclusive. (That sounds harder than it is! If x is 3, then all we’re saying is that in the set {1, 2, 3}, there are 3 numbers.) Now, back to {1, 2, 3, …, x}. Since the average equals the sum divided by the number of numbers, the sum equals the average times that number of numbers. So 1 + 2 + 3 + … + x = Average × Number = [(x + 1)/2]x Finally, to get the original sum, x + 2x + 3x + … + x^2, we just multiply by x again to get x^2(x + 1)/2. Plugging numbers:Pick x = 2. The sum of multiples of 2 from 2 to 2^2 is just 2 + 4 = 6. Check the answers: (A) 2(3)(1) = 6 (B) 2^2(3 + 1)/2 = 6 (C) 2^2(21)=4 (D) (2^3 + 2*2)/2 = 6 (E) 2(21)^2=2 Okay, all we can eliminate is C and E. Try x = 3. The sum of multiples of 3 from 3 to 3^2 is just 3 + 6 + 9 = 18. Check the remaining answers: (A) 3(4)(2) = 24 (B) 3^2(3 + 1)/2 = 18 (D) (3^3 + 2*3)/2 = 16.5
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Re: If x is a positive integer greater than 1, what is the sum of the mult
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06 Sep 2015, 06:10
Bunuel wrote: If x is a positive integer greater than 1, what is the sum of the multiples of x from x to x^2, inclusive?
(A) x(x + 1)(x1) (B) x^2(x + 1)/2 (C) x^2(x1) (D) (x^3 + 2x)/2 (E) x(x1)^2
Kudos for a correct solution. Let, x=2 sum of the multiples of x from x (i.e. 2) to x^2 (i.e. 2^2=4), inclusive = 2+4 = 6 @x=2 (A) x(x + 1)(x1) = 2*3*1 = 6 (B) x^2(x + 1)/2 = 2^2*3/2 = 6(C) x^2(x1) = 2^2*3 = 12(D) (x^3 + 2x)/2 = (8+4)/2 = 6(E) x(x1)^2 = 2*1 = 2i.e. Possible Options are only A, B and D Now, Let, x=3 Sum of the multiples of x from x (i.e. 3) to x^2 (i.e. 3^2=9), inclusive = 3+6+9 = 18@x=3 (A) x(x + 1)(x1) = 3*4*2 = 24 (B) x^2(x + 1)/2 = 3^2*4/2 = 18(D) (x^3 + 2x)/2 = (27+6)/2 = 33/2 i.e. Answer Option B
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Re: If x is a positive integer greater than 1, what is the sum of the mult
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11 Jan 2017, 04:45
Here is what i did in this one =>Putting x=5 Sum = 5+10+15+20+25=75 only option that matches is B.
Hence B.
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Re: If x is a positive integer greater than 1, what is the sum of the mult
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16 Jan 2017, 17:48
Bunuel wrote: If x is a positive integer greater than 1, what is the sum of the multiples of x from x to x^2, inclusive?
(A) x(x + 1)(x1) (B) x^2(x + 1)/2 (C) x^2(x1) (D) (x^3 + 2x)/2 (E) x(x1)^2 Since we know that x is a positive integer greater than 1, we can let x = 2. Thus, we need to determine the sum of multiples of 2 from 2 to 4 inclusive. We see that the sum of the multiples of 2 is 2 + 4 = 6. Now we need to determine which of the answer choices is equivalent to 6: A) x(x + 1)(x  1) = 2(3)(1) = 6….YES B) x^2(x + 1)/2 = 4(3)/2 = 6….YES C) x^2(x  1) = 4(1) = 4….NO D) (x^3 + 2x)/2 = (8 + 4)/2 = 6….YES E) x(x  1)^2 = 2(1)^2 = 2….NO To decide between the answer choices A, B, and D, we can let x = 3. The multiples of 3 between 3 and 9 inclusive are 3, 6, and 9. We have 3 + 6 + 9 = 18. Let’s plug x = 3 into answer choices A, B, and D and see which one(s) produce 18: A) x(x + 1)(x  1) = 3(4)(2) = 24….NO B) x^2(x + 1)/2 =9(4)/2 = 18….YES D) (x^3 + 2x)/2 = (27 + 6)/2 = 16.5….NO Answer: B
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