December 10, 2018 December 10, 2018 10:00 PM PST 11:00 PM PST Practice the one most important Quant section  Integer properties, and rapidly improve your skills. December 11, 2018 December 11, 2018 09:00 PM EST 10:00 PM EST Strategies and techniques for approaching featured GMAT topics. December 11 at 9 PM EST.
Author 
Message 
TAGS:

Hide Tags

Senior Manager
Joined: 21 Oct 2013
Posts: 419

If P and Q represent the hundreds and tens digits, ..x=8PQ2.
[#permalink]
Show Tags
23 Jun 2014, 08:49
Question Stats:
59% (01:58) correct 41% (01:26) wrong based on 185 sessions
HideShow timer Statistics
If P and Q represent the hundreds and tens digits, respectively, in the fourdigit number x=8PQ2, is x divisible by 8? (1) P=4 (2) Q=0 OE According to Stat. (2), 8P02 will always end with an 02. Remember that For a number to be divisible by 4, the number's last two digits must form a number that is divisible by 4. Since 02 is not a number divisible by 4, the entire number, 8P02 is not divisible by 4. A number that is indivisible by 4 cannot be divisible by 8=4*2, so stat. (2) tells you that the answer to the question stem is a definite "no"  which is sufficient.
If you're not sure, plug in the different digits (09) for P and see for yourself how none of the plugins (8102, 8202, 8302, etc.) yields a number that is divisible by 8.
Official Answer and Stats are available only to registered users. Register/ Login.




Math Expert
Joined: 02 Sep 2009
Posts: 51072

If P and Q represent the hundreds and tens digits, ..x=8PQ2.
[#permalink]
Show Tags
23 Jun 2014, 08:57
goodyear2013 wrote: If P and Q represent the hundreds and tens digits, respectively, in the fourdigit number x=8PQ2, is x divisible by 8? (1) P=4 (2) Q=0 OE According to Stat. (2), 8P02 will always end with an 02. Remember that For a number to be divisible by 4, the number's last two digits must form a number that is divisible by 4. Since 02 is not a number divisible by 4, the entire number, 8P02 is not divisible by 4. A number that is indivisible by 4 cannot be divisible by 8=4*2, so stat. (2) tells you that the answer to the question stem is a definite "no"  which is sufficient.
If you're not sure, plug in the different digits (09) for P and see for yourself how none of the plugins (8102, 8202, 8302, etc.) yields a number that is divisible by 8. If P and Q represent the hundreds and tens digits, respectively, in the fourdigit number x=8PQ2, is x divisible by 8?For a number to be divisible by 2 the last digit must be divisible by 2 (so the last digit must be even); For a number to be divisible by 4 the last two digits must be divisible by 4 (04, 08, 12, 16, ..., 96); For a number to be divisible by 8 the last three digits must be divisible by 8 (008, 012, 016, ..., ); etc. (1) P=4. If Q=0, then the answer is NO, because 402 is not divisible by 8, but if Q=3, then the answer is YES, because 432 is divisible by 8. Not sufficient. (2) Q=0. In this case the last tow digits are 02, so x is not divisible by 4, which means that it's not divisible by 8 either. Sufficient. Answer: B. Hope it's clear.
_________________
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




Manager
Joined: 17 Jul 2013
Posts: 81

Re: If P and Q represent the hundreds and tens digits, ..x=8PQ2.
[#permalink]
Show Tags
24 Jul 2014, 04:31
Bunuel why we are checking for 4 ... why don't the we check directly for divisibility by 8 .. for last three digits



Math Expert
Joined: 02 Sep 2009
Posts: 51072

Re: If P and Q represent the hundreds and tens digits, ..x=8PQ2.
[#permalink]
Show Tags
24 Jul 2014, 04:46



Manager
Joined: 21 Jul 2014
Posts: 125

Re: If P and Q represent the hundreds and tens digits,
[#permalink]
Show Tags
07 Aug 2014, 05:39
goodyear2013 wrote: If P and Q represent the hundreds and tens digits, respectively, in the fourdigit number x=8PQ2, is x divisible by 8?
(1) P=4 (2) Q=0 Here's how I solved this question: I started with statement 2 because it seemed easier to tackle a 0 than a 4. 1) Assuming statement 2, I have to answer: is 8P02 divisible by 8? 2) In doing long division, the first 8 is just a distraction because it will never leave a remainder for the hundreds digit. So I started by just removing it entirely. 3) Now I end up with P02 divisible by 8? 4) I saw that the only multiple of 8 that ends in a "2" is 32. Therefore I would need a "P0" value that leaves a remainder of 3. Since 8 is an even number and so is 0, I know that there is no way for there to be a remainder of 3. Therefore I can say statement 2 is sufficient to answer the question stem: no, X is not divisible by 8. NOTE: This can be tricky, because some people will get to this point and think that because the answer to the question stem is "no" that statement two is not correct. Therein lies the trickery of the data sufficiency. Here, I can eliminate options A, C, E. Now I need to test if statement 1 is sufficient. 1) Assuming statement 1, I have to answer: is 84Q2 divisible by 8? 2) Again I can just exclude the 8 to make my calculations simpler. 3) Now I end up with is 4Q2 divisible by 8? 4) Next, I just plugged in a value to test it. Since I know that a value of 0 definitely makes the number NOT divisible by 8 (discovered from my solving of statement 2), I try to look for a way to make the number divisible by 8. 5) As I did my work for statement 2, I had discovered that I would need there to be a remainder of 3 in the 10s digit to make the number divisible by 8. Well, it looks like I can do that by making Q=3. Therefore, I can say that statement 1 is not sufficient. Correct answer is B.



Manager
Joined: 22 Feb 2009
Posts: 172

If P and Q represent the hundreds and tens digits,
[#permalink]
Show Tags
07 Aug 2014, 20:51
goodyear2013 wrote: If P and Q represent the hundreds and tens digits, respectively, in the fourdigit number x=8PQ2, is x divisible by 8?
(1) P=4 (2) Q=0 (1) P = 4 X = 8000 + 100P+ 10Q + 2 = 8000+ 400 + 10Q + 2 Since 8400 is divisible by 8, (10Q +2) has to be divisible by 8. Q is from 1 to 9. If you check, there are 32 and 72 that satisfy the requirement. So 8432 is divisible by 8 but 8452 is not divisible by 8. (2) Q = 0 X= 8000 + 100P + 2 Same reasoning, (100P+2 ) has to be divisible by 8. P is from 1 to 9. We have, 102, 202,....902. For the numbers to be divisible by 8, they have to be divisible by 4, meaning the last two digits have to be divisible by 4. The last two digits are 02, not divisible by 4. So 8PQ2 is not divisible by 8 > SUFFICIENT. B is the answer.
_________________
......................................................................... +1 Kudos please, if you like my post



Tutor
Joined: 20 Apr 2012
Posts: 99
Location: Ukraine
GMAT 1: 690 Q51 V31 GMAT 2: 730 Q51 V38
WE: Education (Education)

Re: If P and Q represent the hundreds and tens digits,
[#permalink]
Show Tags
07 Aug 2014, 23:41
Criterions of divisibility by 2,4, and 8: 2: the last digit of a number is divisible by 2; 4: the last two digits of a number form the integer divisible by 4 8: the last three digits of a number form the integer divisible by 8In the problem \(x\) is divisible by 2, but we don't know about divisibility by 8. (1) If \(P=4\), we have number \(x=84Q2\), which is divisible by 8 if \(4Q2\) is divisible by 8. The answer depends on \(Q\): if \(Q\) is 0, \(x\) is not divisible by 8, but if \(Q\) is 3, \(x\) is divisible by 8. Insufficient(2) If \(Q=0\), we have number \(x=8P02\), which is not divisible by 4, since \(02\) is not divisible by 4. Hence, \(x\) is not divisible by 8. SufficientThe correct answer is B.
_________________
I'm happy, if I make math for you slightly clearer And yes, I like kudos:)



NonHuman User
Joined: 09 Sep 2013
Posts: 9098

Re: If P and Q represent the hundreds and tens digits, ..x=8PQ2.
[#permalink]
Show Tags
17 Dec 2017, 04:43
Hello from the GMAT Club BumpBot! Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up  doing my job. I think you may find it valuable (esp those replies with Kudos). Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________
GMAT Books  GMAT Club Tests  Best Prices on GMAT Courses  GMAT Mobile App  Math Resources  Verbal Resources




Re: If P and Q represent the hundreds and tens digits, ..x=8PQ2. &nbs
[#permalink]
17 Dec 2017, 04:43






