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

It is currently 22 Aug 2019, 09:34

Close

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
Your Progress

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

Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.

Close

Request Expert Reply

Confirm Cancel

With # and & each representing different digits in the problem below,

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:

Hide Tags

Find Similar Topics 
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 57244
With # and & each representing different digits in the problem below,  [#permalink]

Show Tags

New post 16 Apr 2015, 04:57
00:00
A
B
C
D
E

Difficulty:

  15% (low)

Question Stats:

79% (01:29) correct 21% (02:14) wrong based on 269 sessions

HideShow timer Statistics

Retired Moderator
avatar
B
Status: On a mountain of skulls, in the castle of pain, I sit on a throne of blood.
Joined: 30 Jul 2013
Posts: 302
GMAT ToolKit User Reviews Badge
Re: With # and & each representing different digits in the problem below,  [#permalink]

Show Tags

New post 16 Apr 2015, 06:02
1
Bunuel wrote:
With # and & each representing different digits in the problem below, the difference between #&& and ## is 667. What is the value of &?

#&&
- ##
____
667

(A) 3
(B) 4
(C) 5
(D) 8
(E) 9


100#+(10&-10#)+(&-#)=667
89#+11&=667

The only form of 667-89x (where x is an integer) divisible by 11 is when x=7
Therefore, #=7 and &=4

89(7)+11(4)=623+44=667

Answer: B
Manager
Manager
User avatar
Joined: 03 Sep 2014
Posts: 75
Concentration: Marketing, Healthcare
Re: With # and & each representing different digits in the problem below,  [#permalink]

Show Tags

New post 16 Apr 2015, 06:48
1
Bunuel wrote:
With # and & each representing different digits in the problem below, the difference between #&& and ## is 667. What is the value of &?

#&&
- ##
____
667

(A) 3
(B) 4
(C) 5
(D) 8
(E) 9


With subtraction principal, on the units place & - # = 7 and and tens place & - # = 6 this means & is smaller than # so it borrows from the tens digit and subsequently hundred's digit. Now Hundred's digit is # and the result is 6, which is left after the tens digit borrowed 1 from it => # = 7

Thus, at unit place, & - # = 7 => & - 7 = 7 => & was 14 as it borrowed from the tens digit; this means its actual value is 4

Hence, B is the answer
Director
Director
User avatar
Joined: 07 Aug 2011
Posts: 511
Concentration: International Business, Technology
GMAT 1: 630 Q49 V27
GMAT ToolKit User
Re: With # and & each representing different digits in the problem below,  [#permalink]

Show Tags

New post 16 Apr 2015, 06:57
1
Bunuel wrote:
With # and & each representing different digits in the problem below, the difference between #&& and ## is 667. What is the value of &?

#&&
- ##
____
667

(A) 3
(B) 4
(C) 5
(D) 8
(E) 9



Answer B.
744 - 77 = 667
Current Student
User avatar
B
Joined: 25 Nov 2014
Posts: 97
Concentration: Entrepreneurship, Technology
GMAT 1: 680 Q47 V38
GPA: 4
Re: With # and & each representing different digits in the problem below,  [#permalink]

Show Tags

New post 16 Apr 2015, 10:42
2
Did by plugging value.
1) If & = 3, then # becomes 6 but 633 - 66 = 567 not 667. So Not A.
2) If & = 4 then # becomes 7 and 744 - 77 = 667.
Hence B.
_________________
Kudos!!
Senior Manager
Senior Manager
User avatar
B
Joined: 28 Feb 2014
Posts: 294
Location: United States
Concentration: Strategy, General Management
Reviews Badge
Re: With # and & each representing different digits in the problem below,  [#permalink]

Show Tags

New post 16 Apr 2015, 19:23
SherLocked2018 wrote:
Did by plugging value.
1) If & = 3, then # becomes 6 but 633 - 66 = 567 not 667. So Not A.
2) If & = 4 then # becomes 7 and 744 - 77 = 667.
Hence B.


Right on SherLocked2018, used the same method, its faster too
Veritas Prep GMAT Instructor
User avatar
D
Joined: 16 Oct 2010
Posts: 9551
Location: Pune, India
Re: With # and & each representing different digits in the problem below,  [#permalink]

Show Tags

New post 17 Apr 2015, 01:22
1
1
Bunuel wrote:
With # and & each representing different digits in the problem below, the difference between #&& and ## is 667. What is the value of &?

#&&
- ##
____
667

(A) 3
(B) 4
(C) 5
(D) 8
(E) 9


A hint is given in the problem - the hundreds digit of the larger number #&& is # which leads to 6 in the result. So # must be 6 or 7.
But if you subtract 66 from 6&&, you will not get 667 (the largest value you can get is 699 - 66 = 633). So # must be 7.
Now the question is very simple
7&& - 77 = 667
7&& = 667 + 77 = 744

Answer (B)
_________________
Karishma
Veritas Prep GMAT Instructor

Learn more about how Veritas Prep can help you achieve a great GMAT score by checking out their GMAT Prep Options >
Manager
Manager
avatar
Joined: 15 May 2014
Posts: 62
GMAT ToolKit User
Re: With # and & each representing different digits in the problem below,  [#permalink]

Show Tags

New post 18 Apr 2015, 02:14
Rewrite

667
\(\,\)## +
---------
#&&

# could be either \(6\) or \(7\) - if there is a CARRY-OVER
either way there is a CARRY-OVER, so # is \(7\); & is \(4\)

Answer B
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 57244
Re: With # and & each representing different digits in the problem below,  [#permalink]

Show Tags

New post 20 Apr 2015, 05:44
2
1
Bunuel wrote:
With # and & each representing different digits in the problem below, the difference between #&& and ## is 667. What is the value of &?

#&&
- ##
____
667

(A) 3
(B) 4
(C) 5
(D) 8
(E) 9


VERITAS PREP OFFICIAL SOLUTION

Now, many would look at this problem and think “I don’t know how to solve problems like that…”, as it’s not a classic “Algebra” problem, but it’s not a straight-up “Subtraction” problem, either. It uses the common GMAT themes of Abstraction and Reverse-Engineering to test you conceptually to see how you think critically to solve problems. And in true Eminem-mocking form, the key to a complicated-looking problem like this is a lot more mainstream than it is advanced. You have to just get started playing with the numbers, testing possibilities for # and & and seeing what you learn from it.

When GMAT students lament that “I don’t know what tools to use” to start on a tough problem, they’re often missing this piece of GMAT wisdom – *that’s* the point. You’re supposed to look at this with some trial-and-error like you would in a business meeting, throwing some ideas out and eliminating those that definitely won’t work so that you can spend some more time on the ones that have a good chance. In this case, throw out a couple ideas for #. Could # be 5? If it were, then you’d have a number in the 500s and you’d subtract something from it. There’s no way to get to 667 if you start smaller than that and only subtract, so even with pretty limited information you can guarantee that # has to be 6 or bigger.

And by the same logic, try a value like 9 for #. That would give you 900-and-something, and the most that ## could be is 99 (the largest two-digit number), which would mean that your answer would still be greater than 800. You need a number for # that allows you to stay in the 667 range, meaning that # has to be 6 or 7. That means that you’re working with:

6&& – 66 = 667

or

7&& – 77 = 667

And just by playing with numbers, you’ve been able to take a very abstract problem and make it quite a bit more concrete. If you examine the first of those options, keep in mind that the biggest that & can be is 9, and that would leave you with:

699 – 66 = 633, demonstrating that even at the biggest possible value of &, if # = 6 you can’t get a big enough result to equal 667. So, again, by playing with numbers to find minimums and maximums, we’ve proven that the problem has to be:

7&& – 77 = 667, and now you can treat it just like an algebra problem, since the only unknown is now 7&&. Adding 77 to both sides, you get 7&& = 744, so the answer is 4.

More important than this problem, however, is the takeaway – GMAT problems are often designed to look abstract and to test math in a different “order” (here you had two unknowns to “start” the problem and were given the “answer”), and the exam does a masterful job of taking common concepts (this was a subtraction problem) and presenting them to look like something you’ve never seen. The most dangerous mindset you can have on the GMAT quant section is “I don’t know how to solve problems like this” or “I’ve never seen this before”, whereas the successful strategy is to take a look at what you’re given and at least try a few possibilities. With symbol problems (like this), sequence problems, numbers-too-large-to-calculate problems, etc., often the biggest key is to go a lot more mainstream than “advanced math” – try a few small numbers to test the relationship in the problem, and use that to narrow the range of possibilities, find a pattern, or learn a little more about the concept in the problem.

If your standard mindset on abstract-looking problems is “I don’t know how to solve problems like that”, both Em and the G-Em-A-T are right to chide you a bit mockingly, as that’s often the entire point of the problem, to reward those who are willing to try (the entrepreneurial, self-starter types) and “punish” those who won’t think beyond the process they’ve memorized. Even if you don’t become a GMAT God, if you follow some of Eminem’s lessons you can at least find yourself saying “Hi, my name is…” over and over again at b-school orientation.
_________________
Intern
Intern
avatar
Joined: 22 Oct 2018
Posts: 1
With # and & each representing different digits in the problem below,  [#permalink]

Show Tags

New post 12 Nov 2018, 23:32
1
Bunuel wrote:
With # and & each representing different digits in the problem below, the difference between #&& and ## is 667. What is the value of &?

#&&
- ##
____
667

(A) 3
(B) 4
(C) 5
(D) 8
(E) 9


# must be 7 since the difference is given as 667 (hundredths place is 6). Therefore, you have:

7&& - 77 = 667.
7&& = 667 + 77
7&& = 744

Consequently, the answer is (B) 4.
Target Test Prep Representative
User avatar
D
Status: Founder & CEO
Affiliations: Target Test Prep
Joined: 14 Oct 2015
Posts: 7420
Location: United States (CA)
Re: With # and & each representing different digits in the problem below,  [#permalink]

Show Tags

New post 14 Jun 2019, 15:50
1
Bunuel wrote:
With # and & each representing different digits in the problem below, the difference between #&& and ## is 667. What is the value of &?

#&&
- ##
____
667

(A) 3
(B) 4
(C) 5
(D) 8
(E) 9



We see that # (in the hundreds digit) represents either 6 (if there is no borrowing from the tens digit) or 7 (if there is borrowing). However, no matter if it’s 6 or 7, it’s also the tens digit of the subtrahend, and since the tens digit of the difference is also 6, there must be borrowing. So # must be 7. In that case, & (in the tens digit) is either 3 or 4. It can be 3 and by borrowing from 7 (in the hundreds place) becomes 13 and 13 - 7 = 6 (if there is no borrow from the units digit). It can be 4 and by borrowing from 7 (in the hundreds place) and by lending 1 to the units digit becomes 13 and 13 - 7 = 6. We can see which one is correct by checking both cases:

733 - 77 = 656 (This is not correct.)

744 - 77 = 667 (This is correct.)

Answer: B
_________________

Scott Woodbury-Stewart

Founder and CEO

Scott@TargetTestPrep.com
TTP - Target Test Prep Logo
122 Reviews

5-star rated online GMAT quant
self study course

See why Target Test Prep is the top rated GMAT quant course on GMAT Club. Read Our Reviews

If you find one of my posts helpful, please take a moment to click on the "Kudos" button.

Director
Director
User avatar
D
Joined: 24 Oct 2016
Posts: 502
GMAT 1: 670 Q46 V36
GMAT 2: 690 Q47 V38
With # and & each representing different digits in the problem below,  [#permalink]

Show Tags

New post 19 Jul 2019, 15:58
Bunuel wrote:
With # and & each representing different digits in the problem below, the difference between #&& and ## is 667. What is the value of &?

#&&
- ##
____
667

(A) 3
(B) 4
(C) 5
(D) 8
(E) 9



TL;DR



# can only be 6 or 7
If # = 6 => 6&& = 667 + 66 = 7.. (Not possible) => # = 7

7&& = 667 + 77 = 744 => & = 4


Veritas Prep Official Solution



Solution: The big picture: A two digit number is subtracted from a three digit number to give 667. So the three digit number must be a bit larger than 667. This means that the hundreds digit of #&& must be either 6 or 7. It cannot be 8 because you cannot obtain 800+ by adding a two digit number to 667.

Let’s look at both cases:

# is 6: If you subtract 66 from 6&&, you will not get 667 – the largest value you can get is 699 – 66 = 633. So # cannot be 6.

# must be 7.

Now the question is very simple

7&& – 77 = 667

7&& = 667 + 77 = 744
_________________
Most Comprehensive Article on How to Score a 700+ on the GMAT (NEW)
Verb Tenses Simplified


If you found my post useful, KUDOS are much appreciated. Giving Kudos is a great way to thank and motivate contributors, without costing you anything.
GMAT Club Bot
With # and & each representing different digits in the problem below,   [#permalink] 19 Jul 2019, 15:58
Display posts from previous: Sort by

With # and & each representing different digits in the problem below,

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  





Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne