In the correctly-worked multiplication problem above, each symbol repr

Question

https://gmatclub.com/forum/download/file.php?id=26556 In the correctly-worked 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 . AlphameticPost3.jpg

Bunuel · Accepted Answer

VERITAS PREP OFFICIAL SOLUTION:

We multiply two two-digit 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.

suryaabs · Answer

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.

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.

kunals31 · Answer

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.

EMPOWERgmatRichC · Answer

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 NON-0 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

hanyhamdani · Answer

Sol : factorize 1995 : 3x5x7x19 for multiplication : either D OR B must be 5, otherwise we cant get 199 5 and 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 21 Either 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

Madhavi1990 · Answer

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 re-read 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

bumpbot · Answer

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