DS doubts

[nehakhas1]

If M a positive integer , then M ^3 has how many digits ?
1) M has 3 digits .
2) M^2 has 5 digits .
Ans : e while I thought its c

Last year in a group of 30 businesses, 21 reported a net profit and
15 had investments in foreign markets. How many of the businesses
did not report a net profit nor invest in foreign markets last year?
(1) last year 12 of the 30 businesses reported a net profit and had investments in foreign markets.
(2) last year 24 of the 30 businesses reported a net profit or invested in foreign markets, or both.

Ans : b
If the average (arithmetic mean) of the assessed values
of x houses is $212,000 and the average of the assessed
values of y other houses is $194,000, what is the average
of the assessed values of the x+y houses?
(1) x+y=36
(2) x=2y

Ans C I still think its b .

Please solve .Thanks in advance

[electrico]

Stmnt 1:

Lets say M= 100 => M^3 = 1000000
but if M= 999 => M^3 = 997002999

Not enoufht to conclude

Stmnt2:

M^2 = 5 digit

Lets say M = 100 => M^2 = 10000 (5 digt)
but M^3 = 1000000

but if M = 300, then M^2 = 90000 -- 5 digit
but M^3 = 27000000

not enough to conclude


Hence E.

[aj5105]

Good solution electrico.

Statement (1)
We can make things a little simpler by choosing M = 100 & M = 300

[GMATQuantCoach]

If M a positive integer , then M ^3 has how many digits ?
1) M has 3 digits .
2) M^2 has 5 digits .
Ans : e while I thought its c

Last year in a group of 30 businesses, 21 reported a net profit and
15 had investments in foreign markets. How many of the businesses
did not report a net profit nor invest in foreign markets last year?
(1) last year 12 of the 30 businesses reported a net profit and had investments in foreign markets.
(2) last year 24 of the 30 businesses reported a net profit or invested in foreign markets, or both.

Ans : b
If the average (arithmetic mean) of the assessed values
of x houses is $212,000 and the average of the assessed
values of y other houses is $194,000, what is the average
of the assessed values of the x+y houses?
(1) x+y=36
(2) x=2y

Ans C I still think its b .

Please solve .Thanks in advance

The first question.
1)Pick the smallest 3 digit number which is M = 100 = 10^2. M^3 = 100^3 = (10^2)^3 = 10^6 which is 7 digits. Now pick the largest 3 digit number. M = 999. Let's round it up to 1000 for the ease of calculation. 1000 = 10^3. (1000)^3 =(10^3)^3 = 10^9. 999^3 should be a bit less than 1000^3. That means 999^3 will have 9 digits instead of 10. Hence it is not sufficient.

2)Still use M = 100 as one case. M^3 will have 7 digits. Let M = 300 (M^2 = 90000) M^3 = (3 * 10^2) ^3 = 27 * 10^6 which has 8 digits. Therefore not sufficient.

When combining the two, use the same example in case 2. E is your answer.


The second question.

Make a table
Net profit | Not net profit Total
--------------------------------------------------------------
Foreign | 15
-------------------------------------------------------------
Non-foreign |
--------------------------------------------------------------
Total 21 30

The question is asking for the non-foreign and no net profit cell. You get the idea.


Problem 3
The total value of x and y houses combined is 212x + 194y. The question is asking for (212x + 194y)/(x+y).

I have to agree with you on that one. B is the answer

[vittalgmat]

I got a PM to respond to Q 1.

My solution is very similar to Electrico. I dont want to take anything away from his excellent explanation.

The takeaways from this problem are:
1. squares and cubes of numbers have diff number of digits, the digits increase as the value of M increases.
2. Not easy to tell how many digits cube of a number has even if we know number of digits in the number and its square.

Ht Helps
-V