January 26, 2019 January 26, 2019 07:00 AM PST 09:00 AM PST Attend this webinar to learn how to leverage Meaning and Logic to solve the most challenging Sentence Correction Questions. January 27, 2019 January 27, 2019 07:00 AM PST 09:00 AM PST Attend this webinar to learn a structured approach to solve 700+ Number Properties question in less than 2 minutes.
Author 
Message 
TAGS:

Hide Tags

Math Expert
Joined: 02 Sep 2009
Posts: 52431

Which of the following is two more than the square of an odd integer?
[#permalink]
Show Tags
02 Sep 2015, 21:54
Question Stats:
61% (02:19) correct 39% (02:32) wrong based on 158 sessions
HideShow timer Statistics




Math Expert
Joined: 02 Sep 2009
Posts: 52431

Re: Which of the following is two more than the square of an odd integer?
[#permalink]
Show Tags
06 Sep 2015, 04:42
Bunuel wrote: Which of the following is two more than the square of an odd integer?
(A) 14,173 (B) 14,361 (C) 14,643 (D) 14,737 (E) 14,981
Kudos for a correct solution. MANHATTAN GMAT OFFICIAL SOLUTION:From the size of the answer choices, we should recognize that there must be some trick – a way to find the answer quickly within 2 minutes, since theoretically, every GMAT problem must be solvable that way. Let’s start from first principles. We can represent a general odd integer as 2k + 1, where k is an integer. So the square of an odd integer can be written this way: (2k + 1)^2 = 4k^2 + 4k + 1 Since the first two terms (4k^2 and 4k) contain 4 as a factor, we can see that they are both multiples of 4, and thus their sum is also a multiple of 4. This means that the square of any odd integer is 1 more than a multiple of 4. Thus, the number we are looking for (“two more than the square…”) is 3 more than a multiple of 4. To quickly determine whether a number is a multiple of 4, we can just examine the last 2 digits. The reason is that 100 is divisible by 4, so only the tens and the ones digit matter. The hundreds digit, the thousands digit, etc. will never affect divisibility by 4. Looking at the answer choices and cutting off everything but the last 2 digits, we are left with 73, 61, 43, 37, and 81. Of these, only 43 is 3 more than a multiple of 4 (40). Thus, C is the right answer. (Incidentally, 14,643 is 2 + 121^2.) The correct answer is (C).
_________________
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: 29 Jul 2015
Posts: 158

Re: Which of the following is two more than the square of an odd integer?
[#permalink]
Show Tags
03 Sep 2015, 07:02
Bunuel wrote: Which of the following is two more than the square of an odd integer?
(A) 14,173 (B) 14,361 (C) 14,643 (D) 14,737 (E) 14,981
Kudos for a correct solution. one of the given options should be a square if 2 is subtracted from it. the options would be (A) 14,171 (B) 14,359 (C) 14,641 (D) 14,735 (E) 14,979 We can solve this question with many approaches. Here are the 2 easiest methods. Method 1: If a square has odd unit's digit, then it's ten's digit will always be even. Only 14,641 satisfies this condition. Method 2: If you know about palindromic numbers, then you can clearly see that 14,641 is a palindromic square. Answer: C




Manager
Joined: 10 Aug 2015
Posts: 103

Re: Which of the following is two more than the square of an odd integer?
[#permalink]
Show Tags
03 Sep 2015, 11:00
Solution:First sub 2 from all numbers: 14171 14359 14641 14735 14979 These are closer to 14400 which is 120^2. S0, try 121^2 and you will get 14641 as answer. Option C I know this is crude method and hope that Bunuel will provide a better one.



Manager
Joined: 04 May 2015
Posts: 71
Concentration: Strategy, Operations
WE: Operations (Military & Defense)

Re: Which of the following is two more than the square of an odd integer?
[#permalink]
Show Tags
03 Sep 2015, 12:44
kunal555 wrote: Bunuel wrote: Which of the following is two more than the square of an odd integer?
(A) 14,173 (B) 14,361 (C) 14,643 (D) 14,737 (E) 14,981
Kudos for a correct solution. one of the given options should be a square if 2 is subtracted from it. the options would be (A) 14,171 (B) 14,359 (C) 14,641 (D) 14,735 (E) 14,979 We can solve this question with many approaches. Here are the 2 easiest methods. Method 1: If a square has odd unit's digit, then it's ten's digit will always be even. Only 14,641 satisfies this condition.Method 2: If you know about palindromic numbers, then you can clearly see that 14,641 is a palindromic square. Answer: C Could someone give some background on why the above highlighted is true... I didn't know what
_________________
If you found my post useful, please consider throwing me a Kudos... Every bit helps



Manager
Joined: 10 Aug 2015
Posts: 103

Which of the following is two more than the square of an odd integer?
[#permalink]
Show Tags
03 Sep 2015, 14:58
DropBear wrote: kunal555 wrote: Bunuel wrote: Which of the following is two more than the square of an odd integer?
(A) 14,173 (B) 14,361 (C) 14,643 (D) 14,737 (E) 14,981
Kudos for a correct solution. one of the given options should be a square if 2 is subtracted from it. the options would be (A) 14,171 (B) 14,359 (C) 14,641 (D) 14,735 (E) 14,979 We can solve this question with many approaches. Here are the 2 easiest methods. Method 1: If a square has odd unit's digit, then it's ten's digit will always be even. Only 14,641 satisfies this condition.Method 2: If you know about palindromic numbers, then you can clearly see that 14,641 is a palindromic square. Answer: C Could someone give some background on why the above highlighted is true... I didn't know what Please find attached for the proof. I like doing on paper than typing. That's why i have taken a pic and attached it. Hope I was helpful.
Attachments
IMG_0198.JPG [ 1.86 MiB  Viewed 1988 times ]



Intern
Joined: 12 Nov 2013
Posts: 40

Re: Which of the following is two more than the square of an odd integer?
[#permalink]
Show Tags
05 Sep 2015, 10:14
Bunuel wrote: Which of the following is two more than the square of an odd integer?
(A) 14,173 (B) 14,361 (C) 14,643 (D) 14,737 (E) 14,981
Kudos for a correct solution. If 2 is subtracted from the numbers in the option, we will get a square of an odd integer. The numbers are closer to square of 120, 120 x120 = 14400 try 121, you get 14641. option C = 14643  2 = 14641
_________________
Kindly support by giving Kudos, if my post helped you!



Board of Directors
Joined: 17 Jul 2014
Posts: 2598
Location: United States (IL)
Concentration: Finance, Economics
GPA: 3.92
WE: General Management (Transportation)

Which of the following is two more than the square of an odd integer?
[#permalink]
Show Tags
06 Mar 2016, 19:12
Bunuel wrote: Which of the following is two more than the square of an odd integer?
(A) 14,173 (B) 14,361 (C) 14,643 (D) 14,737 (E) 14,981
Kudos for a correct solution. wow..now this is smth I had no idea how to approach.. my first calculations = 100x100 = 10,000 so def need smth 12X*120X, otherwise I would not get 14XXX and def smth less than 130x130 =because we get 16,900 so only options are: 121, 123, 125, 127, 129. so started with 121*121 => 14,641  which is 2 less than C..



Manager
Joined: 14 Oct 2012
Posts: 165

Which of the following is two more than the square of an odd integer?
[#permalink]
Show Tags
Updated on: 30 Oct 2016, 09:46
Summary: All perfect squares end in 1, 4, 5, 6, 9 or 00 (i.e. Even number of zeros). Therefore, a number that ends in 2, 3, 7 or 8 is not a perfect square. Digital roots are 1, 4, 7 or 9. No number can be a perfect square unless its digital root is 1, 4, 7, or 9. You might already be familiar with computing digital roots. (To find digital root of a number, add all its digits. If this sum is more than 9, add the digits of this sum. The single digit obtained at the end is the digital root of the number.) If unit digit ends in 5, ten’s digit is always 2. If it ends in 6, ten’s digit is always odd (1, 3, 5, 7, and 9) otherwise it is always even. That is if it ends in 1, 4, and 9 the ten’s digit is always even (2, 4, 6, 8, 0). Total numbers of prime factors of a perfect square are always odd
Source: burningmath blogspot com_2013_09_howtocheckifnumberisperfectsquare



Senior Manager
Joined: 13 Oct 2016
Posts: 367
GPA: 3.98

Which of the following is two more than the square of an odd integer?
[#permalink]
Show Tags
30 Oct 2016, 07:44
According to the question we have: (2x+1)^2=y2 4x^2+4x+3=y => 4(x^2+x)+3=y So y is 3 more than a multiple of 4. Now check our options for divisibility by 4: 1) 733=70 No. 2) 613=58 No. 3) 433=40 Yes. 4) 373=34 No. 5) 813=78 No. We have choice C.



NonHuman User
Joined: 09 Sep 2013
Posts: 9462

Re: Which of the following is two more than the square of an odd integer?
[#permalink]
Show Tags
18 Apr 2018, 08:33
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: Which of the following is two more than the square of an odd integer? &nbs
[#permalink]
18 Apr 2018, 08:33






