GMAT Math

Hi,

Can some1 please answer the answers and concepts behind these DS Questions?

Question 1. Are all of the numbers in a certain list of 15 numbers equal?
1. The sum of all the numbers in the list is 60.
2. The sum of any three numbers in the list is 12.

Question 2. Beginning in January of last year, Carl made deposits of $120 into his account on the 15th of each month for several consecutive months and then made withdrawals of $50 from the account on the 15th of each of the remaining months of last year. There were no other transactions in the account last year. If the closing balance of Carl's account for May of last year was $2,600, ehat was the range of the monthly closing balances of Carl's account last year.
1. Last year the closing balance of Carl's account for April was less than $2,625.
2. Last year the closing balance of Carl's account for June was less than $2,675.


Question 3. If N is a positive integer, what is the tens digit of N?
1. The hundreds digit of 10N is 6.
2. The tens digit of N+1 is 7.

Question 1. Are all of the numbers in a certain list of 15 numbers equal?
1. The sum of all the numbers in the list is 60.
2. The sum of any three numbers in the list is 12.

Stmt 1: The sum of all the numbers in the list is 60.
if 14 numbers are 1 and 15th number is 46, then sum is 60
if 15 numbers are all equal to 4, still sum is 60.
Hence we have 2 or more instances where the statement holds good. So not sufficient to answer the question.

2. The sum of any three numbers in the list is 12.
This is only possible if all numbers are equal.

If the numbers are 0,5,7,0,5,7.... then sum of 5,7 and 7 is not equal to 12.
The only way sum of any randomly picked numbers will be 12 is if all the numbers are equal.
this this statement alone helps us answer the question. Hence B.

Question 3. If N is a positive integer, what is the tens digit of N?
1. The hundreds digit of 10N is 6.
2. The tens digit of N+1 is 7.

1. The hundreds digit of 10N is 6.
Sufficient.
suppose N = 61
10N = 610
hundreds of 10N is 6. which is the same as tens digit of N.


2. The tens digit of N+1 is 7
Not sufficient.
N = 70
N+1 = 71, then 10s digit of N+1 is 7 and tens digit of N is 7.
N=69
N+1 = 70. then 10s digit of N+1 is 7 and tens digit of N is 6.

Hence this statement is not enough to answer the question.

Hence answer is A.

Beginning in January of last year, Carl made deposits of $120 into his account on the 15th of each month for several consecutive months and then made withdrawals of $50 from the account on the 15th of each of the remaining months of last year. There were no other transactions in the account last year. If the closing balance of Carl's account for May of last year was $2,600, ehat was the range of the monthly closing balances of Carl's account last year.
1. Last year the closing balance of Carl's account for April was less than $2,625.
2. Last year the closing balance of Carl's account for June was less than $2,675.

to find range of values , we need to know exact balances at the end of each month. Given data that he initially put 120 each month.. then stopped and started withdrawing 50 from a certain month. If we find the month that he stopped putting 120 and started taking 50 out, then that data is sufficient to find the range. (We dont need to actually find the range)
1. Last year the closing balance of Carl's account for April was less than $2,625.

So in May he either added 120 or withdrew 50 and reached 2600 in the end of May. If he withdrew 50, it means in the end of April it must be 2650. But statement says it was less than 2625. So he definitely added 120 (from 2480) to reach 2600. But we dont know what we did in June.
So the given data allows us to find that until May he was adding 120 each. So we can find the starting of January value. (We dont need to calculate it)


2. Last year the closing balance of Carl's account for June was less than $2,675.

Using a logic similar to that used in statement 1 (don carry info from statement 1 to 2 here.) end of May 2600. He either added 120 or deleted 50. If he added 120, then balance must be 2720, but statemen says it was less than 2675. This means he withdrew 50. but we dont know what he did in the previous months. So we can find the the exact amounts till December but dont know what he did in Jan-May period.
NOT Sufficient.

Combining 1 and 2. Now the above 2 calculations give us exactly all the end of month balances for the entire year allowing us to find the range. So combined statements are sufficient. Hence the answer is C.