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The product of two negative numbers is 160. If the lesser of the two [#permalink]
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15 Jun 2016, 01:31
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Re: The product of two negative numbers is 160. If the lesser of the two [#permalink]
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15 Jun 2016, 03:33
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a*b =160 1
a=(2b)4 2
substituting eq 2 in 1
(2b4)*b=160 2b^2+4b160=0 b^2+2b80=o b^2+10b8b80=0 b= 10,8 therefore b =8
substitute the value in eq 2 a = 164= 20
therefore the larger number = 8



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Re: The product of two negative numbers is 160. If the lesser of the two [#permalink]
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15 Jun 2016, 04:27
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Bunuel wrote: The product of two negative numbers is 160. If the lesser of the two numbers is 4 less than twice the greater, what is the greater number?
A) 20 B) 16 C) 10 D) 8 E) 4 let two numbers are a and b a = 2b4 Find value of b. (2b4)*b = 160 b*(b2) = 80 b =8 (Given that numbers are negative) D is the answer.



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Re: The product of two negative numbers is 160. If the lesser of the two [#permalink]
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15 Jun 2016, 04:49
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Bunuel wrote: The product of two negative numbers is 160. If the lesser of the two numbers is 4 less than twice the greater, what is the greater number?
A) 20 B) 16 C) 10 D) 8 E) 4 Consider two negative numbers as \(n_1\) and \(n_2\). \(n_1 * n_2 = 160\) \(n_2 = 2n_1  4\) ..... substitute this in above equation. \(n_1 * (2n_1  4) = 160\) \(2n_1^2  4n_2  160 = 0\) \(n_1^2  2n_2  80 = 0\) \((n_1  10) (n_1 +8) = 0\) \(n_1 = 10\) and \(n_1 = 8\) as mentioned in question, numbers are negative, we'll consider \(n_1 = 8\). substitute this in second equation. \(n_2 = 2 * (8)  4\) \(n_2 = 20\) Hence the greater number is \(8\). \(Answer = D\)



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Re: The product of two negative numbers is 160. If the lesser of the two [#permalink]
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19 Jul 2016, 12:23
Confused about this.. The quadratic gives us two roots: (larger #)= 10 and (larger #)= +8 Curious why we didn't choose 10 since (although it is the smaller number between the roots, it is the only negative number.. and the question said that both numbers are negative). Say we chose 10, then 10 x 16 also equals 160 and in this case 10 is in fact the larger number. I'm sure I'm missing something since everyone got D.. can someone please tell me why D and not C? Thanks in advance!



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Re: The product of two negative numbers is 160. If the lesser of the two [#permalink]
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19 Jul 2016, 12:28
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nk18967 wrote: Confused about this.. The quadratic gives us two roots: (larger #)= 10 and (larger #)= +8 Curious why we didn't choose 10 since (although it is the smaller number between the roots, it is the only negative number.. and the question said that both numbers are negative). Say we chose 10, then 10 x 16 also equals 160 and in this case 10 is in fact the larger number. I'm sure I'm missing something since everyone got D.. can someone please tell me why D and not C? Thanks in advance! Hi! There, We get the quadratic as x^2 2x 80= 0 (x+8) (x10)= 0 x can either be 8 or +10. But because it is given that the numbers are ve, we will choose 8. Hope it is clear.
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Re: The product of two negative numbers is 160. If the lesser of the two [#permalink]
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19 Jul 2016, 13:04
Thanks Divyadisha! Just realized what a silly mistake I made! I had let the smaller # be (a) and let the larger # be (b).. (a) = 2(b)  4 (a)(b) = 160 So I solved it as: [2(b)  4] [b] = 160 [2b  4] [b] = 160 2b^2 + 4b  160 = 0 b^2 + 2b  80 = 0 (b8) (b+10) So, b= 8 or b= 10 Here is where I forgot, that my number is actually (b) !!!! That changes things because then my number can be either (8) or (10)...which is +10.. SO... the Ans is obviously 8 since we need a ve #!! I hope I dont make these kind of mistakes when I'm taking the real test! Ugh..! Divyadisha wrote: nk18967 wrote: Confused about this.. The quadratic gives us two roots: (larger #)= 10 and (larger #)= +8 Curious why we didn't choose 10 since (although it is the smaller number between the roots, it is the only negative number.. and the question said that both numbers are negative). Say we chose 10, then 10 x 16 also equals 160 and in this case 10 is in fact the larger number. I'm sure I'm missing something since everyone got D.. can someone please tell me why D and not C? Thanks in advance! Hi! There, We get the quadratic as x^2 2x 80= 0 (x+8) (x10)= 0 x can either be 8 or +10. But because it is given that the numbers are ve, we will choose 8. Hope it is clear.



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Re: The product of two negative numbers is 160. If the lesser of the two [#permalink]
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19 Jul 2016, 22:53
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Bunuel wrote: The product of two negative numbers is 160. If the lesser of the two numbers is 4 less than twice the greater, what is the greater number?
A) 20 B) 16 C) 10 D) 8 E) 4 Use the options. The options give you the greater number. Start from the middle option. (C)  10 Twice of 10 is 20 and 4 less is 24. 24 * 10 = 240 (Not correct) We need lower product (of 160) so try option (D). (D)  8 Twice of 8 is 16 and 4 less is 20. 20 * 8 = 160 Correct Answer (D)
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Re: The product of two negative numbers is 160. If the lesser of the two [#permalink]
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24 Sep 2016, 08:21
Two factors of 160 can be (1,160), (2,80), (4,40), (8, 20), (16,10), (32, 5). Considering the relation, lower = 2 higher 4, we can eliminate everything other than (8,20) and (16, 10) and the answer would be (8, 20) i.e. 8



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Re: The product of two negative numbers is 160. If the lesser of the two [#permalink]
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06 Dec 2016, 08:28
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Bunuel wrote: The product of two negative numbers is 160. If the lesser of the two numbers is 4 less than twice the greater, what is the greater number?
A) 20 B) 16 C) 10 D) 8 E) 4 We are given that the product of two negative numbers is 160 and that the lesser of the two numbers is 4 less than twice the greater. We can let x = the larger number and y = the smaller number, and we can create the following equations: (x)(y) = 160 AND y = 2x  4 Substituting (2x  4) for y in the first equation yields: x(2x  4) = 160 2x^2 + 4x = 160 x^2  2x  80 = 0 (x  10)(x + 8) = 0 x = 10 or x = 8 Since x is negative, x = 8 and y = 2(8) 4 = 20. Thus, the greater number is 8. Answer: D
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The product of two negative numbers is 160. If the lesser of the two [#permalink]
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06 Dec 2016, 12:41
Bunuel wrote: The product of two negative numbers is 160. If the lesser of the two numbers is 4 less than twice the greater, what is the greater number?
A) 20 B) 16 C) 10 D) 8 E) 4 1. xy=160 2. x=2y4 dividing 1. by 2.➡ y^22y80=0 y=8 D



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Re: The product of two negative numbers is 160. If the lesser of the two [#permalink]
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07 Dec 2016, 11:22
Bunuel wrote: The product of two negative numbers is 160. If the lesser of the two numbers is 4 less than twice the greater, what is the greater number?
A) 20 B) 16 C) 10 D) 8 E) 4 \(a*b = 160\) Let a > b So, b = 2a  4 Or, a( 2a  4 ) = 160 Or, 2a^2 + 4a = 160 Or, 2a ( a + 2 ) = 16*10 Or, a = 8 So, b = 20 Thus, the greater number is (D) 8
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Re: The product of two negative numbers is 160. If the lesser of the two [#permalink]
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09 Oct 2017, 20:25
i think i did this a little different than most people above. first, broke 160 down into pairs (below): 1, 160 2, 80 4, 40 5, 32 8, 20 10, 16 NOW, remember the question tells you that the LOWER # is 4 less than TWICE the greater? > L=2S+4Okay, let's see which #s (from list above) make sense... 1, 160 2, 80 4, 40 5, 32 8, 2010, 16Don't follow my logic? Well, let's set S=8. L=16+4. So, if S=8, L=20. Perfect fit. > Don't fall for the trap: 10, 16. Here, if S=10, then L=24 [aka 2*10+4]kudos please if you find this helpful



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Re: The product of two negative numbers is 160. If the lesser of the two [#permalink]
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09 Oct 2017, 22:15
Do the answer checking method,
8*2  4 = 20
So greater number should be 8 Answer D



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Re: The product of two negative numbers is 160. If the lesser of the two [#permalink]
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15 Oct 2017, 08:47
Bunuel wrote: The product of two negative numbers is 160. If the lesser of the two numbers is 4 less than twice the greater, what is the greater number?
A) 20 B) 16 C) 10 D) 8 E) 4 x = lesser y = greater (2y4)(y) = 160 a , b , and c are too high values, so eliminate them For e, (12)(4) =/ 160 For D, (164)(8) = (20)(8) = 160 Therefore, D)8 is the answer



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Re: The product of two negative numbers is 160. If the lesser of the two [#permalink]
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18 Nov 2017, 04:26
ScottTargetTestPrep wrote: Bunuel wrote: The product of two negative numbers is 160. If the lesser of the two numbers is 4 less than twice the greater, what is the greater number?
A) 20 B) 16 C) 10 D) 8 E) 4 We are given that the product of two negative numbers is 160 and that the lesser of the two numbers is 4 less than twice the greater. We can let x = the larger number and y = the smaller number, and we can create the following equations: (x)(y) = 160 AND y = 2x  4 Substituting (2x  4) for y in the first equation yields: x(2x  4) = 160 2x^2 + 4x = 160 x^2  2x  80 = 0 (x  10)(x + 8) = 0 x = 10 or x = 8 Since x is negative, x = 8 and y = 2(8) 4 = 20. Thus, the greater number is 8. Answer: D hello there it says product of two negative numbers than why you write (x)(y) = 160 shouldn't it be (x)(y) = 160 Also how after this x^2  2x  80 = 0 you get (x  10)(x + 8) = 0 I know formula B^2  4AC but couldn't use it properly, though I didn't divide whole equation by 2. Also after this (x  10)(x + 8) = 0
you write that x = 10 or x = 8 > but how can x=10? if in brackets it is 10 and how can x = 8 if in brackets 8 is positive
thanks for taking time to explain and have a great day!



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Re: The product of two negative numbers is 160. If the lesser of the two [#permalink]
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11 Jan 2018, 15:48
Hi All, This question can be solved by TESTing THE ANSWERS. We can also use a bit of logic to eliminate some of the work. We're told that the product of 2 NEGATIVE numbers is 160. We're told that the LESSER of the two numbers is "4 less than twice" the GREATER value. We're asked for that greater value. Before we do any work, it's worth noting that a "greater" negative number is the one that's CLOSER to 0. As an example... 1 is GREATER than 1,000 Thus, the correct answer is almost certainly going to be C, D or E. Let's TEST Answer D.... Answer D: 8 IF the greater value is 8, then the lesser values is (2)(8)  4 = 16  4 = 20 Since (8)(20) does equal +160, then this is an exact match for what we're looking for  and this MUST be the answer! Final Answer: GMAT assassins aren't born, they're made, Rich
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