Problem Solving

The sum of the digits of integer A is 170. A = 10^(14)-B; What is B?

40, 45, 50, 55, 60

GMAC frowns upon posting live questions, to say the least. I have a feeling this is one. I hope I am wrong!

should i post the gmatfocus pic to prove its a gmatfocus question? or do you suggest I pay 200 bucks an hour to get a tutor like yourself?

I only wish I could charge $200 an hour! I'm sorry to say that GMAT instructors don't earn very much in Spain...

I was simply alerting you to the fact that GMAC takes copyright infringement seriously. Some people have posted live questions without realizing that they are jeopardizing their MBA future in doing so.

If it is a GMATFocus question, you should type the question word for word so that we can answer it.

If it were a live question, I think we could ask a moderator to delete it for you. Keep in mind that GMAC reviews forums for live questions!

thailandvc wrote:should i post the gmatfocus pic to prove its a gmatfocus question? or do you suggest I pay 200 bucks an hour to get a tutor like yourself?

hahahahahhahahahahhaha....I like you

Though I found a similar question in one of the other forums, I am unable to crack this...
Maybe some one else can solve along these lines...

https://gmatclub.com/forum/750-level-gpr ... 72947.html

@thailandvc - R u sure the below question is correct ?

The sum of the digits of integer A is 170. A = 10^(14)-B; What is B?

40, 45, 50, 55, 60

10^(14) - 15 digits ..leaving the last two digits - we have 12 * 9 = 108

108 + 10 (Taking into account the max sum possible with the option 45) = 118

Just to add to the explanation given above,

10^14 = 100000000000000

if you subtract a 2 digit number from this figure, you get

999999999999(10/9)(10/0) - AB (the two digit number)

Since we have to find the sum of the digits, 9*12 = 108

Now solving for the given options

1) 40 ---> 108 + 6 + 0 = 114
2) 45 -----> 108 + 5 + 5 = 118
3) 50 ----> 108 +5+0 = 113
4) 55-----> 108 + 4+5 = 117
5) 60 ----> 108 + 4 +0 = 112

Sadly, 170 cannot be the answer. :twisted:

Simply put. 10 (to the power 14) - X is at the most a 14 digit number with all 9s (when x=1)

14*9 = 126 is the maximum value a 14 digit number can take. So the question itself is not valid. Like the person who has worked it out, none of the answers substituted to the question gives a 170!

Also,

Using another simple rule which is very handy in a lot of problems. Any number when added with 9, the sum of digits does
not change. for eg. 8 or 17 or 26 or -1.

Sum of digits = 170, or Further adding, 1 + 7 is 8.
Sum of digits of 10^14 is 1 (or 10 using the 9's rule).
So B has to be -1=1-B. B's sum of digits has to be 2 or 11 or something that matches the same.

None of the given options match this.

So these cannot be the answer in any case. (Even if they replaced 170 by a number less than 126 like 107, this rule would prove that the sum of digits simply cannot work for the given options.)

Vineesh, could you please elaborate on how this rule helps solving the problem. I'm losing it from the "So b has to be -1=1-B" portion. Thanks!

vineeshp wrote: Using another simple rule which is very handy in a lot of problems. Any number when added with 9, the sum of digits does
not change. for eg. 8 or 17 or 26 or -1.

Sum of digits = 170, or Further adding, 1 + 7 is 8.
Sum of digits of 10^14 is 1 (or 10 using the 9's rule).
So B has to be -1=1-B. B's sum of digits has to be 2 or 11 or something that matches the same.

None of the given options match this.

So these cannot be the answer in any case. (Even if they replaced 170 by a number less than 126 like 107, this rule would prove that the sum of digits simply cannot work for the given options.)

Before I get into that, you should simply look at the fact that a 14 digit number cannot have the sum of digits as 170. So the question itself is wrong. End of story.
----------------------------------------------------
Since u r reading this portion, I assume you wanna risk looking at my complex way. ( )
Using the rule, the sum of digits of B has to be 8=1-B. (all represent sum of digits.)

U can write 8 as -1 as it is -1 off 9.
Similarly, If the sum of digits is 3, u can either look at it as 3 or 12 (3+9) or 21(3 +9+) or -6 (3-9).
or 1 can be represented as 1 or 10 or 19. (Sum of digits is 1 in each case.)

so sum of digits of So 170 = 10^14 - B can be written as

8=10-B

which means B has to be 2 (or 11 or 21 or so on)
None of the answer choices have that.

Note: If 55 was 56, then we had atleast a chance of referring that, substituting in the equation and getting the value of X and checking if it matches the value of A.