The sum of the digits of a three-digit number is 11. What is the produ

Question

The sum of the digits of a three-digit number is 11. What is the product of the three digits?

(1) The number is divisible by 5.
(2) The hundreds digit is twice the tens digit.

Kudos for a correct  solution .

ENGRTOMBA2018 · Answer

Let the number be abc. Given : a+b+c =11

1. Per statement 1, the number is divisible by 5. The possible values are 830, 425 etc.  The product can thus be 8*3*0=0 or 4*2*5 = 40 . Thus this statement is not sufficient.

2. Per statement 2, the possible values are 425, 632, 218 .  The product can be 4*2*5=40 or 6*3*2=36 or 2*1*8=16 . Thus this statement is not sufficient.

Combining 1 and 2 , the only number that is divisible by 5 and has hundred's digit twice of the ten's digit = 425 and the product is 40. Thus C is the correct answer.

GMATinsight · Answer

Given : Sum of The digits = 11

Question : What is the product of the three digits of a Three digit Number?

Statement 1 : The number is divisible by 5.

The three Digit Number could be 920, 830, 720 i.e. Product of Digits = 0
The three Digit Number could be 515, 425, 335 i.e. Product of Digits = 25, 40, 45 respectively
 NOT SUFFICIENT

Statement 2 : The hundreds digit is twice the tens digit. 
Number could be 425 i.e. Product of digits = 40
or Number could be 632 i.e. Product of digits = 36
 NOT SUFFICIENT

Combining the twos statements  
Number Must be a multiple of 5 i.e. Unit digit must be either 0 or
and Hundred's digit must be twice the Ten's digit

i.e. 0 can't be the unit digit as in that case Hundred's digit will NEVER be twice the Ten's digit due to sum of the digits (x+2x+0=3x) being 11 (Non Multiple of 3)
i.e. UNIT DIGIT Must be 5

Now, The only possibility of Number with both conditions satisfied is 425 i.e. Product of Digits = 40
 SUFFICIENT

Answer: Option C

AmoyV · Answer

x+y+z=11 xyz=?

1. z=5 or 0

x and y could be anything and the product could also be anything or 0.
Not Sufficient

2. x=2y
We know nothing about z.

Not Sufficient

1 and 2:
2y+y+5=11 OR 2y+y+0=11
3y=6 OR 3y=11
y can only be 2

Therefore x=4; y=2 and z=5

Answer: C

Sindbad · Answer

Let the no be xyz.
given x+y+z = 11. Value of( x*y*z)=?

from (1) The number is divisible by 5. 
So unit digit will be either 0 or 5 i.e. z=0,5
if z =0 x,y can be only 1,1 ,if z=5 x,y(without ordering) can take up{(3,3),(4,2),(5,1),(6,0)} . Since more than 1 solution .  Not Sufficient

from(2)
hundredth digit is twice tens. i.e. x=2y
the possible values in order (x)(2y)(z) will be {(2)(1)(8),(4)(2)(5),(6)(3)(2)} .Since more than 1 solution .  Not Sufficient

combining (1) and (2) 
only common no is 425 and product is 4*2*5=40  Sufficient ; Hence C

akanksha23 · Answer

Let the number be xyz
Given: x+y+z=11

Statement 1
Divisible by x means z=0 or 5
So we have many possibilities
Number can be 245,920, 425 and so on and we don't get one value of product xyz
Hence not sufficient

Statement 2
x=2y
2y+y+z=11 
3y+z =11
And with this we can have number as 218, 425 and 632
Hence not sufficient

Combining 1 & 2
We want a number to be divisible by 5 and should also satisfy 2nd statement 
Hence the number is 425 and hence distinct value of product 
Answer C

EMPOWERgmatRichC · Answer

Hi Engr2012,

Your thinking in regards to this question is great and your solution is correct, but when dealing with the individual Facts you did NOT actually answer the question that was asked.

I bring this up because, with a Q49, you clearly know your math rules, patterns and tactics...but with a little more work you could hit Q50 or Q51. In your situation, the missing points are going to come down to a few 'little things' (likely involving work that you choose not to do (or that you do in your head)). In certain DS questions, your attention-to-detail will matter MORE than your 'math skills' (which is one of the many reasons why DS questions are designed the way they are).

Since you're still posting in these Forums with a 690/Q49, I assume that you're planning to retake the GMAT with the goal of scoring higher. I believe that you can certainly do that, but you have to add a slightly higher level of detail and precision to your work.

GMAT assassins aren't born, they're made,
Rich

ENGRTOMBA2018 · Answer

Hi  EMPOWERgmatRichC , thank you for the comment. Yes, I do intend to re-appear for GMAT. Can you please explain what all details are you talking about that I have missed? You also mention that I did not actually answer the question. I did mention the final unique product of the digits and the correct answer choice. I do agree that the reason why I did not hit 50 or 51 in my earlier attempts was that I must have missed those little and important details. Finally, it will help me immensely, if you could elaborate further on your last sentence "I believe that you can certainly do that, but you have to add a slightly higher level of detail and precision to your work." by citing example of the above problem.

NB: I have updated the solution

Thanks

EMPOWERgmatRichC · Answer

Hi Engr2012,

The easiest examples to find (about what I'm describing) can be found in your practice CATs. After taking each CAT, you should do a full review of your work. When you get a question wrong, it's important to try to define WHY you got the question wrong. How many of those questions were 'gettable' BUT you made a silly/little mistake? To take it a step further, what COULD you have done to keep that little mistake from happening? Usually the 'answer' to that last question is to take slightly more notes (or better organized notes). That might be something that you can practice on your own, but it might require learning a new way to 'see' (and respond to) the Test.

GMAT assassins aren't born, they're made,
Rich

Bunuel · Answer

800score Official Solution:

Statement (1) alone is not sufficient because it tells us only that the number has a units digit of 0 or 5. If the number has a units digit of 0, the product of the digits will be 0 (since 0 times any number is 0), and if the number has a units digit of 5, the product of the digits might not be zero (depending on whether one of the other digits is 0). For instance, the number 515 has digits that add to 11, yet the product of the digits is 25. Therefore, Statement (1) is insufficient.

Statement (2) is not sufficient by itself either. The number could be 218 or 425 or 632. The product of the digits is different in each case.

Combined, the two statements are sufficient. The only possibility is that the number is 425, and the product of the digits is 40.

Since the statements are both insufficient individually but sufficient when combined,  the correct answer is choice (C) .

Bunuel · Answer

Similar question to practice: the-three-digits-of-a-number-add-up-to-11-the-number-is-div-158329.html

bumpbot · Answer

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