GMAT Question of the Day - Daily to your Mailbox; hard ones only

 It is currently 15 Jul 2018, 14:30

### GMAT Club Daily Prep

#### Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

# (6^3)a+(6^2)b+6c+d=821, where a, b, c, and d

Author Message
TAGS:

### Hide Tags

Math Revolution GMAT Instructor
Joined: 16 Aug 2015
Posts: 5825
GMAT 1: 760 Q51 V42
GPA: 3.82
(6^3)a+(6^2)b+6c+d=821, where a, b, c, and d [#permalink]

### Show Tags

19 Oct 2017, 00:04
00:00

Difficulty:

85% (hard)

Question Stats:

57% (01:41) correct 43% (02:22) wrong based on 72 sessions

### HideShow timer Statistics

[GMAT math practice question]

(6^3)a+(6^2)b+6c+d=821, where a, b, c, and d are integers from 0 to 5, inclusively, c=?

A. 0
B. 1
C. 2
D. 3
E. 4

_________________

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" "Free Resources-30 day online access & Diagnostic Test" "Unlimited Access to over 120 free video lessons - try it yourself" BSchool Forum Moderator Joined: 26 Feb 2016 Posts: 2931 Location: India GPA: 3.12 (6^3)a+(6^2)b+6c+d=821, where a, b, c, and d [#permalink] ### Show Tags 19 Oct 2017, 00:22 This expression can be written as 216a + 36b + 6c + d. The value of the expression must be 821 and a,b,c, and d must have integer values, and we have been asked to find the value of c. The value of the expression must be closest to 821 using values of a,b,c,d! If a=3,b=4, the sum of 216a + 36b will be: 216*3 = 648 | 36*4 = 144 | 648+144 = 792. 6c + d must be 27, which is only possible when c=4(Option E) since d cannot be greater than 5. _________________ You've got what it takes, but it will take everything you've got Intern Joined: 29 May 2012 Posts: 39 Re: (6^3)a+(6^2)b+6c+d=821, where a, b, c, and d [#permalink] ### Show Tags 19 Oct 2017, 01:28 Not sure if my approach is the most appropriate one, but just to share... (6^3)a+(6^2)b+6c+d=216a + 36b + 6c + d=821 Because all a, b, c, and d are integers from 0 to 5, the largest possible value for a is 3; therefore, 648 + 36b + 6c +d=821 and 36b + 6c +d = 173; The largest possible value for b is then 4; therefore, 144 + 6c +d = 173 and 6c + d = 29; Therefore, the largest possible value for c is 4. Answer is E. Math Expert Joined: 02 Sep 2009 Posts: 46991 Re: (6^3)a+(6^2)b+6c+d=821, where a, b, c, and d [#permalink] ### Show Tags 19 Oct 2017, 02:12 MathRevolution wrote: [GMAT math practice question] (6^3)a+(6^2)b+6c+d=821, where a, b, c, and d are integers from 0 to 5, inclusively, c=? A. 0 B. 1 C. 2 D. 3 E. 4 Similar question: https://gmatclub.com/forum/7-3-a-7-2-b- ... 48834.html _________________ Director Joined: 14 Nov 2014 Posts: 662 Location: India Schools: Rotman '20 (S) GMAT 1: 700 Q50 V34 GPA: 3.76 Re: (6^3)a+(6^2)b+6c+d=821, where a, b, c, and d [#permalink] ### Show Tags 19 Oct 2017, 09:55 MathRevolution wrote: [GMAT math practice question] (6^3)a+(6^2)b+6c+d=821, where a, b, c, and d are integers from 0 to 5, inclusively, c=? A. 0 B. 1 C. 2 D. 3 E. 4 As given Value is 821 (6^3)a+(6^2)b+6c---- even and divisible by 6 ------------------1 D must be odd .----------------------------------2 D can be 1 , 3, or 5 let D = 1 = (6^3)a+(6^2)b+6c = 820 ---this is not possible as 820 is not divisible by 6 (as per condition 1) D = 3 =(6^3)a+(6^2)b+6c = 818 ---this is also not possible as 818 is not divisible by 6 D = 5 =(6^3)a+(6^2)b+6c = 816 --yes , only possible value for (6^3)a+(6^2)b+6c 216 * 3 + 36 * 4 + 6 * 4 = 816 C = 4 ---- SC Moderator Joined: 22 May 2016 Posts: 1824 (6^3)a+(6^2)b+6c+d=821, where a, b, c, and d [#permalink] ### Show Tags 20 Oct 2017, 00:12 MathRevolution wrote: [GMAT math practice question] (6^3)a+(6^2)b+6c+d=821, where a, b, c, and d are integers from 0 to 5, inclusively, c=? A. 0 B. 1 C. 2 D. 3 E. 4 $$(6^3)a + (6^2)b+ 6c+ d=821$$ $$(216)a + (36)b+ 6c + d = 821$$ At most, c = 5, d = 5 At most, 6c + d = 35 So nearly 800 has to be from 216a and 36b. Further: 216 must carry most of the weight. For example, if a = 2, then 216a = 432. Even if b, c, and d = 5, the last three terms cannot sum to 432. So: Maximize 216a, with 821 as limit 821/216 = 3.xx a = 3 (216 * 3) = 648 Remaining? 821 - 648 = 173 Maximize 36b, with 173 as limit 173/36 = 4.xx b = 4 (36 * 4) = 144 Remaining? 173 - 144 = 29 29 = 6c + d d cannot be < 5 If d = 0, 1, 2, 3 or 4, results are 29, 28, 27, 26, and 25. They are not multiples of 6 required by 6c d = 5 (29 - 5) = 24 c = 4 6c = 24 (6c + d) = (24 + 5) = 29 That works. c = 4 Answer E _________________ In the depths of winter, I finally learned that within me there lay an invincible summer. -- Albert Camus, "Return to Tipasa" Math Revolution GMAT Instructor Joined: 16 Aug 2015 Posts: 5825 GMAT 1: 760 Q51 V42 GPA: 3.82 Re: (6^3)a+(6^2)b+6c+d=821, where a, b, c, and d [#permalink] ### Show Tags 22 Oct 2017, 21:20 => 821 = 6*136 + 5 136 = 6*22 + 4 22 = 6*3 +4 821 = 6*136 + 5 = 6*(6*22+4) + 5 = 6 * ( 6 * (6 *3 + 4) + 4 ) + 5 = 6 * ( 6^2*3 + 6*4 + 4 ) + 5 = 6^3*3 + 6^2*4 + 6*4 + 5 = 6^3*a + 6^2*b + 6*c + d Thus a = 3, b = 4, c = 4 and d = 5. Therefore, the answer is E. Answer: 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"
"Free Resources-30 day online access & Diagnostic Test"
"Unlimited Access to over 120 free video lessons - try it yourself"

Re: (6^3)a+(6^2)b+6c+d=821, where a, b, c, and d   [#permalink] 22 Oct 2017, 21:20
Display posts from previous: Sort by

# Events & Promotions

 Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne Kindly note that the GMAT® test is a registered trademark of the Graduate Management Admission Council®, and this site has neither been reviewed nor endorsed by GMAC®.