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100 points for $49 worth of Veritas practice GMATs FREE VERITAS PRACTICE GMAT EXAMS Earn 10 Points Per Post Earn 10 Points Per Thanks Earn 10 Points Per Upvote ## If x, y, and d are integers and d is odd, are both x and y tagged by: BTGmoderatorLU ##### This topic has 2 expert replies and 1 member reply ### Top Member ## If x, y, and d are integers and d is odd, are both x and y ## Timer 00:00 ## Your Answer A B C D E ## Global Stats Difficult Source: GMAT Paper Tests If x, y, and d are integers and d is odd, are both x and y divisible by d? 1) x+y is divisible by d. 2) x-y is divisible by d. The OA is C ### GMAT/MBA Expert GMAT Instructor Joined 22 Aug 2016 Posted: 1984 messages Followed by: 30 members Upvotes: 470 BTGmoderatorLU wrote: Source: GMAT Paper Tests If x, y, and d are integers and d is odd, are both x and y divisible by d? 1) x+y is divisible by d. 2) x-y is divisible by d. The OA is C Given: x, y, and d are integers and d is odd We have to find out whether x, y, and d are integers and d is odd. Let's take each statement one by one. 1) x + y is divisible by d. Case 1: Say x = 5, y = 1 and d =3 x + y = 5 + 1 = 6; we see that 6 is divisible 3, but neither x nor y is divisible by d. The answer is No. Case 2: Say x = 6, y = 3 and d =3 x + y = 6 + 3 = 9; we see that 9 is divisible 3, and both x are y divisible by d. The answer is Yes. Insufficient. 2) x - y is divisible by d. Case 1: Say x = 5, y = 2 and d =3 x - y = 5 - 2 = 3; we see that 3 is divisible 3, but neither x nor y is divisible by d. The answer is No. Case 2: Say x = 6, y = 3 and d =3 x - y = 6 - 3 = 3; we see that 3 is divisible 3, and both x are y divisible by d. The answer is Yes. Insufficient. (1) and (2) together We see that Case 1 of both the statements cannot exist here; thus, the answer is yes, both x and y are divisible by d. The correct answer: C Hope this helps! -Jay _________________ Manhattan Review LSAT Prep Locations: Manhattan GMAT | Free GRE Practice Questions | LSAT Prep Courses London | SAT Prep Courses Dubai | and many more... Schedule your free consultation with an experienced GMAT Prep Advisor! Click here. ### GMAT/MBA Expert GMAT Instructor Joined 08 Dec 2008 Posted: 13001 messages Followed by: 1250 members Upvotes: 5254 GMAT Score: 770 BTGmoderatorLU wrote: Source: GMAT Paper Tests If x, y, and d are integers and d is odd, are both x and y divisible by d? 1) x+y is divisible by d. 2) x-y is divisible by d. The OA is C Given: x, y, and d are integers and d is odd Target question: Are both x and y divisible by d? Statement 1: x+y is divisible by d. Let's TEST some values. There are several values of x, y and d that satisfy statement 1. Here are two: Case a: x = 6, y = 9 and d = 3. Notice that 6+9 = 15, and 15 is divisible by 3. In this case, the answer to the target question is YES, x and y ARE both divisible by d Case b: x = 2, y = 4 and d = 3. Notice that 2+4 = 6, and 6 is divisible by 3. In this case, the answer to the target question is NO, x and y are NOT both divisible by d Since we cannot answer the target question with certainty, statement 1 is NOT SUFFICIENT Statement 2: x-y is divisible by d Let's TEST some values. Case a: x = 9, y = 3 and d = 3. Notice that 9-3 = 6, and 6 is divisible by 3. In this case, the answer to the target question is YES, x and y ARE both divisible by d Case b: x = 10, y = 4 and d = 3. Notice that 10-4 = 6, and 6 is divisible by 3. In this case, the answer to the target question is NO, x and y are NOT both divisible by d Since we cannot answer the target question with certainty, statement 2 is NOT SUFFICIENT Statements 1 and 2 combined Here are some nice divisibility rules: Rule #1. If integers A and B are each divisible by integer k, then (A + B) is divisible by k Rule #2. If integers A and B are each divisible by integer k, then (A - B) is divisible by k Statement 1 tells us that x+y is divisible by d Statement 2 tells us that x-y is divisible by d By Rule #1, (x+y) + (x-y) is divisible by d Simplify to get: 2x is divisible by d Since we're told that d is ODD, we know that x MUST BE divisible by d By Rule #2, (x+y) - (x-y) is divisible by d Simplify to get: 2y is divisible by d Since we're told that d is ODD, we know that y MUST BE divisible by d So, the answer to the target question is YES, x and y ARE both divisible by d Answer: C Cheers, Brent _________________ Brent Hanneson â€“ Creator of GMATPrepNow.com Use my video course along with Sign up for free Question of the Day emails And check out all of these free resources GMAT Prep Now's comprehensive video course can be used in conjunction with Beat The GMATâ€™s FREE 60-Day Study Guide and reach your target score in 2 months! ### Top Member Legendary Member Joined 02 Mar 2018 Posted: 1121 messages Followed by: 2 members Question --> are both x and y divisible by d? This means that x and y must be a multiple of d STATEMENT 1: x+y is divisible by d $$Let\ \ d\ =3,\ and\ x+y=21$$ # $$Case\ 1:\ If\ x=6\ and\ y=15,\ then\ x\ and\ y\ are\ divisible\ by\ d$$ $$Case\ 2:\ But\ if\ x=1\ and\ y=20,\ both\ x\ and\ u\ are\ not\ divisible\ by\ d$$ $$Therefore,\ statement\ 1\ is\ INSUFFICIENT$$ STATEMENT 2: x-y is divisible by d let d=3 and x-y=21 $$Case\ 1:\ if\ x=25\ and\ y=4,\ then\ x\ and\ y\ are\ not\ divisible\ by\ d$$ $$Case\ 2:\ if\ x=24\ and\ y=3,\ then\ x\ and\ y\ are\ divisible\ by\ d$$ $$Thus,\ statement\ 2\ is\ INSUFFICIENT$$ Combining both statement together; Statement 1 = (x+y)/3 = v ------ (1) Statement 2 = (x-y)/3 = w -------(2) $$From\ \left(2\right),\ x=3w+y$$ $$From\ \left(1\right),\ x+y=3v\ where\ x=3w+y$$ $$3w+y+y=3v$$ $$2y=3\left(v-w\right)\ and\ hence,\ y=\frac{3\left(v-w\right)}{2}$$ Since v and w are whole numbers / integer, then y must be a multiple of 3. x=3w + y where y is a multiple of 3 and x also must be a multiple of 3. Both x and y are divisible by d when both statement are combined together. Therefore, option C is the correct answer • Award-winning private GMAT tutoring Register now and save up to$200

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