Author 
Message 
TAGS:

Hide Tags

Intern
Joined: 22 May 2017
Posts: 5

If x, y and z are integers then is the product of x, y, and z divisibl [#permalink]
Show Tags
Updated on: 21 Jan 2018, 23:14
Question Stats:
78% (01:54) correct 22% (01:28) wrong based on 9 sessions
HideShow timer Statistics
If x, y and z are integers then is the product of x, y, and z divisible by 6? (1) x = y  1 and z = y + 1 (2) x, y, and z are successive multiples of 2 Hello please check the answer and explain the significance? Does the sequence 2,0,2 violate the statement 2??? Attachment:
Doubt.png [ 68.12 KiB  Viewed 296 times ]
Official Answer and Stats are available only to registered users. Register/ Login.
Originally posted by akgulhane on 21 Jan 2018, 21:49.
Last edited by Bunuel on 21 Jan 2018, 23:14, edited 1 time in total.
Renamed the topic and edited the question.



DS Forum Moderator
Joined: 22 Aug 2013
Posts: 1186
Location: India

Re: If x, y and z are integers then is the product of x, y, and z divisibl [#permalink]
Show Tags
21 Jan 2018, 22:40
Hi
In general, when we talk about 'multiples of 2', we mean positive multiples only. So 3 successive multiples of 2 could be (2,4,6) or (4,6,8) or (1002,1004,1006) etc.
But still even if you look at 2,0,2 their product is 0 which is divisible by 6 (0 is divisible by all numbers except 0, resulting in 0 only)



Senior Manager
Joined: 17 Oct 2016
Posts: 326
Location: India
Concentration: Operations, Strategy
GPA: 3.73
WE: Design (Real Estate)

Re: If x, y and z are integers then is the product of x, y, and z divisibl [#permalink]
Show Tags
21 Jan 2018, 23:21
I have a query here. as per statement 1, we can conclude that x, y and z are successive numbers. like 1,2,3 or 4,5,6 or 77,78,79 and so on. but as per statement 2 they are consecutive multiples of 2, which means they are 2,4,6 or 88,86,84. Doesn't st1 and st2 contradicts each other and they are against the general rule of DS questions? Need some expert reply
_________________
Help with kudos if u found the post useful. Thanks



Math Expert
Joined: 02 Sep 2009
Posts: 46129

If x, y and z are integers then is the product of x, y, and z divisibl [#permalink]
Show Tags
21 Jan 2018, 23:28
akgulhane wrote: If x, y and z are integers then is the product of x, y, and z divisible by 6? (1) x = y  1 and z = y + 1 (2) x, y, and z are successive multiples of 2 Hello please check the answer and explain the significance? Does the sequence 2,0,2 violate the statement 2??? Attachment: Doubt.png If x, y and z are integers then is the product of x, y, and z divisible by 6?(1) x = y  1 and z = y + 1. In this case xyz = (y  1)y(y + 1) = the product of three consecutive integers, so at least one of them must be even and one of them must be a multiple of 3, so the product for sure will be a multiple of 6. Sufficient. Or you can recall following property: The product of n consecutive integers is always divisible by n!. Thus, the product of three consecutive integers, must be divisible by 3! = 6. (2) x, y, and z are successive multiples of 2 > xyz = (2k  2)2k(2k + 2) = 8*(k  1)k(k + 1). The same here: (k  1)k(k + 1) = the product of three consecutive integers, so the product for sure will be a multiple of 6. Sufficient. Technically the answer should be D, as EACH statement ALONE is sufficient to answer the question. But even though formal answer to the question is D (EACH statement ALONE is sufficient), this is not a realistic GMAT question, as: on the GMAT, two data sufficiency statements always provide TRUE information and these statements never contradict each other or the stem. (1) says that x, y and z are consecutive integers, while (2) says that x, y and z are EVEN consecutive integers. The statement clearly contradict each other, which cannot happen. So, the question is flawed. You won't see such a question on the test. As for you question: 0 is a multiple of every integer, so 0 IS a multiple of both 2 (0 is even) and 6. Finally, you tagged this question as GMAT Prep, which is NOT true. Please, read carefully and follow our rules of posting: https://gmatclub.com/forum/rulesforpo ... 33935.html Thank you.
_________________
New to the Math Forum? Please read this: Ultimate GMAT Quantitative Megathread  All You Need for Quant  PLEASE READ AND FOLLOW: 12 Rules for Posting!!! Resources: GMAT Math Book  Triangles  Polygons  Coordinate Geometry  Factorials  Circles  Number Theory  Remainders; 8. Overlapping Sets  PDF of Math Book; 10. Remainders  GMAT Prep Software Analysis  SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS)  Tricky questions from previous years.
Collection of Questions: PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.
What are GMAT Club Tests? Extrahard Quant Tests with Brilliant Analytics




If x, y and z are integers then is the product of x, y, and z divisibl
[#permalink]
21 Jan 2018, 23:28






