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# The product of 4 consecutive odd integers is negative. What is the lar

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Math Revolution GMAT Instructor
Joined: 16 Aug 2015
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The product of 4 consecutive odd integers is negative. What is the lar  [#permalink]

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17 Jul 2018, 01:11
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[GMAT math practice question]

The product of 4 consecutive odd integers is negative. What is the largest odd integer?

1) The smallest integer is negative.
2) The third smallest integer is negative.

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"Only $99 for 3 month Online Course" "Free Resources-30 day online access & Diagnostic Test" "Unlimited Access to over 120 free video lessons - try it yourself" PS Forum Moderator Joined: 25 Feb 2013 Posts: 1201 Location: India GPA: 3.82 The product of 4 consecutive odd integers is negative. What is the lar [#permalink] ### Show Tags 17 Jul 2018, 01:24 MathRevolution wrote: [GMAT math practice question] The product of 4 consecutive odd integers is negative. What is the largest odd integer? 1) The smallest integer is negative. 2) The third smallest integer is negative. Let the odd integers be $$a,b,c,d$$ in ascending order. We need the value of $$d$$ Given: $$a*b*c*d<0$$. Hence either one or three numbers are negative Statement 1: implies $$a<0$$ but we know nothing about other numbers. if $$c<0$$, then $$d=1$$ but if $$b,c,d>0$$, then $$d=5$$. Insufficient Statement 2: implies that $$c<0$$, therefore $$a,b,c<0$$ and $$d>0$$ or $$d=1$$. Sufficient Option B Math Expert Joined: 02 Aug 2009 Posts: 6544 Re: The product of 4 consecutive odd integers is negative. What is the lar [#permalink] ### Show Tags 17 Jul 2018, 01:42 MathRevolution wrote: [GMAT math practice question] The product of 4 consecutive odd integers is negative. What is the largest odd integer? 1) The smallest integer is negative. 2) The third smallest integer is negative. 4 consecutive ODD integers Product is negative : ONLY when one or three of them are negative A) only one... -1,1,3,5 B) three of them -5,-3,-1,1 Let us see the statements 1) the smallest integer is negative.. Both cases have smallest integer as negative.. Insufficient 2) the third smallest integer is negative. Only possibility - case (B) So largest number is 1 Sufficient B _________________ 1) Absolute modulus : http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372 2)Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html 3) effects of arithmetic operations : https://gmatclub.com/forum/effects-of-arithmetic-operations-on-fractions-269413.html GMAT online Tutor Director Status: Learning stage Joined: 01 Oct 2017 Posts: 501 WE: Supply Chain Management (Energy and Utilities) Re: The product of 4 consecutive odd integers is negative. What is the lar [#permalink] ### Show Tags 17 Jul 2018, 02:15 MathRevolution wrote: [GMAT math practice question] The product of 4 consecutive odd integers is negative. What is the largest odd integer? 1) The smallest integer is negative. 2) The third smallest integer is negative. Let the 4 consecutive odd integers be 2n-3, 2n-1, 2n+1, and 2n+3. Smallest:- 2n-3 Largest:- 2n+3 Given, (2n-3)(2n-1)(2n+1)(2n+3)<0----(a) St1:- (2n-3)<0 Or, n<1.5 So, we can have more than one value of 2n+3. (at n=-1, n=1) Insufficient. St2:- (2n+1)<0 Or, n< -0.5----------(b) only n=-1 satisfies both (a) & (b). So, largest: 2n+3=2(-1)+3=1 Sufficient. Ans. (B) _________________ Regards, PKN Rise above the storm, you will find the sunshine CEO Joined: 12 Sep 2015 Posts: 2705 Location: Canada Re: The product of 4 consecutive odd integers is negative. What is the lar [#permalink] ### Show Tags 17 Jul 2018, 08:28 Top Contributor MathRevolution wrote: The product of 4 consecutive odd integers is negative. What is the largest odd integer? 1) The smallest integer is negative. 2) The third smallest integer is negative. Target question: What is the largest odd integer? Given: The product of 4 consecutive odd integers is negative. It's worth taking the time to analyze what this is telling us. If the product of 4 consecutive odd integers is negative, then there are only 2 possible scenarios: Scenario #1: The numbers are -5, -3, -1, 1 (the product is -15, which is negative) Scenario #2: The numbers are -1, 1, 3, 5 (the product is -15, which is negative) Now let's check the statements: Statement 1: The smallest integer is negative Notice that BOTH scenarios meet this condition In scenario #1, the answer to the target question is the largest integer is 1 In scenario #2, the answer to the target question is the largest integer is 5 Since we cannot answer the target question with certainty, statement 1 is NOT SUFFICIENT Statement 2: The third smallest integer is negative Only scenario #1 meets this condition So, the answer to the target question is the largest integer is 1 Since we can answer the target question with certainty, statement 2 is SUFFICIENT Answer: B Cheers, Brent _________________ Brent Hanneson – Founder of gmatprepnow.com Math Revolution GMAT Instructor Joined: 16 Aug 2015 Posts: 6028 GMAT 1: 760 Q51 V42 GPA: 3.82 Re: The product of 4 consecutive odd integers is negative. What is the lar [#permalink] ### Show Tags 19 Jul 2018, 02:26 => Forget conventional ways of solving math questions. For DS problems, the VA (Variable Approach) method is the quickest and easiest way to find the answer without actually solving the problem. Remember that equal numbers of variables and independent equations ensure a solution. The first step of the VA (Variable Approach) method is to modify the original condition and the question. We then recheck the question. Since we have 1 variable (n) and 0 equations, D is most likely to be the answer. So, we should consider each of the conditions on their own first. Let the integers be $$2n – 3, 2n – 1, 2n + 1$$ and $$2n +3.$$ Since $$(2n-3)(2n-1)(2n+1)(2n+3) < 0,$$ either one of the integers is negative, or three of the integers is negative. There are two possible lists of integers: $$-1, 1, 3, 5$$ and $$-5, -3, -1, 1.$$ Condition 1) The largest odd integers in the two possible lists are $$5$$ and $$1$$. Since we don’t have a unique answer, condition 1) is not sufficient. Condition 2) If the third smallest integer is negative, then the integers are $$-5, -3, -1, 1.$$ The largest integer is $$1$$. Since we have a unique answer, condition 2) is sufficient. Therefore, B is the answer. Answer: B If the original condition includes “1 variable”, or “2 variables and 1 equation”, or “3 variables and 2 equations” etc., one more equation is required to answer the question. If each of conditions 1) and 2) provide an additional equation, there is a 59% chance that D is the answer, a 38% chance that A or B is the answer, and a 3% chance that the answer is C or E. Thus, answer D (conditions 1) and 2), when applied separately, are sufficient to answer the question) is most likely, but there may be cases where the answer is A,B,C or E. _________________ MathRevolution: Finish GMAT Quant Section with 10 minutes to spare The one-and-only World’s First Variable Approach for DS and IVY Approach for PS with ease, speed and accuracy. "Only$99 for 3 month Online Course"
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Re: The product of 4 consecutive odd integers is negative. What is the lar &nbs [#permalink] 19 Jul 2018, 02:26
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