November 18, 2018 November 18, 2018 07:00 AM PST 09:00 AM PST Get personalized insights on how to achieve your Target Quant Score. November 18th, 7 AM PST November 20, 2018 November 20, 2018 09:00 AM PST 10:00 AM PST The reward for signing up with the registration form and attending the chat is: 6 free examPAL quizzes to practice your new skills after the chat.
Author 
Message 
TAGS:

Hide Tags

Math Expert
Joined: 02 Sep 2009
Posts: 50622

In the correctlyworked multiplication problem above, each symbol repr
[#permalink]
Show Tags
06 May 2015, 01:36
Question Stats:
27% (02:22) correct 73% (02:40) wrong based on 341 sessions
HideShow timer Statistics




Math Expert
Joined: 02 Sep 2009
Posts: 50622

Re: In the correctlyworked multiplication problem above, each symbol repr
[#permalink]
Show Tags
11 May 2015, 03:43
Bunuel wrote: In the correctlyworked multiplication problem above, each symbol represents a different nonzero digit. What is the value of C? (1) D is prime. (2) B is not prime. Kudos for a correct solution.Attachment: AlphameticPost3.jpg VERITAS PREP OFFICIAL SOLUTION:We multiply two twodigit integers and get 1995. The good thing is that we know the result of the multiplication will be 1995. Usually, multiplication alphametics are harder since they involve multiple levels, but here the multiplication is actually a blessing. There are many many ways in which you can ADD two integers to give 1995 but there are only a few ways in which you can multiply two integers to give you 1995. Let’s prime factorize 1995: 1995 = 3*5*7*19 We can probably count on our fingers the number of ways in which we can select AB and CD. 19 needs to be multiplied with one other factor to give us a two digit number since 5*3*7 = 105 (a three digit number) so AB and CD cannot be 19 and 105. 19*3 = 57, 5*7 = 35 – This is not possible since two of the four digits are same here – 5. 19*5 = 95, 3*7 = 21 – This is one option for AB and CD. 19*7 = 133 – Three digit number not possible. Hence AB and CD can only take values out of 21 and 95. As of now, C can be 2 or 9. We need to find whether the given statements give us a unique value of C. Statement 1: D is prime D is the units digit of CD. So D can be 1 or 5. 1 is not prime so CD cannot be 21. Hence, CD must be 95 and AB must be 21. Hence, C must be 9. This statement alone is sufficient. Statement 2: B is not prime If B is not prime then AB cannot be 95. Hence AB must be 21. This means CD will be 95 and C will be 9. This statement alone is sufficient. Answer (D) Note that the entire question was just about number properties – prime factors, prime numbers etc. Actually it required no iterative steps and no hit and trial. Rest assured that if it is a GMAT question, it will be reasoning based and will not require painful calculations.
_________________
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




Intern
Joined: 08 Jan 2015
Posts: 3

Re: In the correctlyworked multiplication problem above, each symbol repr
[#permalink]
Show Tags
06 May 2015, 03:53
Since the last digit of the product is 5, either B or D has to be 5.
Statement 1  D is Prime. D can be 5, but can also be 3 or 7. This statement is insufficient.
Statement 2  B is not prime. This statement implies that B is not 5, so D has to be 5. Now, 1995 is perfectly divisible by 05, 15, 35 and 95. 05 is not acceptable as per the condition given in the question. 15 will also be rejected, as AB will then need to be 133. 35 is also rejected, as AB will be 57, but all the digits are distinct.
Thus, only remaining option is 95 (95*21). All conditions are satisfied and C will be 9.
Answer  B.



Intern
Joined: 27 Mar 2015
Posts: 1

Re: In the correctlyworked multiplication problem above, each symbol repr
[#permalink]
Show Tags
06 May 2015, 17:34
AB x CD = 1995... breaking 1995 into its prime factors  3 x 5 x 7 x 19.. looking to find combinations of 2 digits from this 4 prime factors, will lead to only possibility of 21 x 95 i.e., other options are not possible like 35 x 57... 5 repeats here.. other 2 possibilities result in 3 digit numbers..
statement (1) D is prime.. meaning D=5 only possibility.. hence sufficient
statement (2) B is not prime.. meaning B=1 only possibility.. hence sufficient
Hence D.



EMPOWERgmat Instructor
Status: GMAT Assassin/CoFounder
Affiliations: EMPOWERgmat
Joined: 19 Dec 2014
Posts: 12871
Location: United States (CA)

Re: In the correctlyworked multiplication problem above, each symbol repr
[#permalink]
Show Tags
11 May 2015, 17:06
Hi kunals31, You made a nice deduction when dealing with Fact 1, but in DS questions you have to factor in ALL of the information that you're given (AND answer the question that's asked) before you can state that a Fact is sufficient or insufficient. Here, we're told that each of the 4 letters represents a DIFFERENT NON0 digit. Given the possibilities that you've described, what would each letter in the final equation be? Would there be ANY DUPLICATES (because that's NOT allowed according to the prompt)...? Sometimes DS questions require a couple of extra "steps" to prove what the correct answer is. As you score higher and higher in the Quant section, you're more likely to come across questions that require a bit more work. GMAT assassins aren't born, they're made, Rich
_________________
760+: Learn What GMAT Assassins Do to Score at the Highest Levels Contact Rich at: Rich.C@empowergmat.com
Rich Cohen
CoFounder & GMAT Assassin
Special Offer: Save $75 + GMAT Club Tests Free
Official GMAT Exam Packs + 70 Pt. Improvement Guarantee www.empowergmat.com/
*****Select EMPOWERgmat Courses now include ALL 6 Official GMAC CATs!*****



Intern
Status: preparing
Joined: 30 Dec 2013
Posts: 40
Location: United Arab Emirates
Concentration: Technology, Entrepreneurship
GMAT 1: 660 Q45 V35 GMAT 2: 640 Q49 V28 GMAT 3: 640 Q49 V28 GMAT 4: 640 Q49 V28 GMAT 5: 640 Q49 V28
GPA: 2.84
WE: General Management (Consumer Products)

Re: In the correctlyworked multiplication problem above, each symbol repr
[#permalink]
Show Tags
12 Dec 2016, 12:02
Bunuel wrote: In the correctlyworked multiplication problem above, each symbol represents a different nonzero digit. What is the value of C? (1) D is prime. (2) B is not prime. Kudos for a correct solution.Attachment: AlphameticPost3.jpg Sol : factorize 1995 : 3x5x7x19 for multiplication : either D OR B must be 5, otherwise we cant get 199 5and both numbers must be TWO digit numbers. Either : 19x3= 57 so 2 numbers will be 57 and 35 ( but all digits must be distinct as stated) or 19x5=95 so 2 numbers will be 95 and 21Either AB = 95 or CD=95 Stmnt 1) D is prime so CD = 95 : since 1 not prime so c=9 Sufficient Stmnt 2: B is not prime : same CD= 95 Sufficient D is answer. My kudos please



Senior Manager
Joined: 15 Jan 2017
Posts: 359

Re: In the correctlyworked multiplication problem above, each symbol repr
[#permalink]
Show Tags
08 May 2018, 22:15
Took about 4 minutes to do this one, but was using hit and trial. Many thanks to the succinct solutions above. My method is as follows: 1995 > to get a 5 in unit's place, we need 7*5, 9*5, 3*5
(1) D is prime.
> thus, D has to be 3,5,7. Factorization of 1995 gives = 19*7*3*5 > out of this only one combination 35*57 has D as prime. But, when I reread the question, we CANNOT repeat the numbers. So only fits >the other one 21*95, has one of them composite, one prime and no repeats (2) B is not prime. > this was one easier > only 21*95 fits.
So picked D.
Kudos, if you found this useful




Re: In the correctlyworked multiplication problem above, each symbol repr &nbs
[#permalink]
08 May 2018, 22:15






