Hi, I have difficulty to solve the following math problems from Indian website. Can you guys help me figure them out?
Thank you very much.
Good luck to everyone!!!!!

ORKUT QUANTDATABASE (Till Aug 7th)

1. If standard deviation of 'p' number of people is 21.5 and standard deviation of 'q' number of people is 9 then what is that least possible standard deviation value when both p and q are added?

4. How many of the following 2, 4, -7, sqrt(19) & 8 have their square 4 more than the multiples of 5?
A. 0
B. 1
C. 2
D. 3
E. 4

5. If A1, A2, A3, A4 & A5 belongs to a series such that An= n{(-1)^n -1}, then what will be the difference of the largest and the smallest term?
A. 4
B. 6
C. 8
D. 10
E. 12

6. If R1 = -3,-2,-1
R2 = 1, 2, 3 &
R3 = -3, -2, -1, 1, 2, 3
and if s1, s2 ans s3 are standard deviations of R1, R2 and R3 then which of the following is true?
i. s1<S2
ii. s2<0
iii. s3=0

A. NONE
B. i only
C. ii only
D. iii only
E. all three

7. In a class of certain number of students, if 1/2 of the students takes maths as their major, 2/3 takes physics as their major & 1/3 takes both maths and physics as their majors and if 40 students didn't take any of maths or physics subjects as their major then what is the total number of students in the class?

8. If x < y then
Col A: x^2+x+1
Col B: y^2+y+1


12. Given a line in xy plane with slope k = -1/2
Col A: x-intercept
Col B: y-intercept

ORKUT QUANTDATABASE (Till Aug 6th)

1. What is the remainder of the following (7^0 + 7^1 + 7^2 + 7^3 + ........ + 7^23)/14 ?

8. A person went to market with a red and a green bag and bought 10 carrots & 6 radishes. On the way to home he distributed vegetables into the two bags in such a way that no bag is empty. In how many ways can he do ths?

9. In how many ways, the letters of the word POLLOLOP can be arranged?

10. If 60% children like cats, 70% like dogs and 80% like rabbits then exactly how many children like all three animals?

11. A figure was given, it had a rectangular box in which 16 cylindrical cans, each with radius of 1 inch are placed. If the cans touch adjacent cans and/or the walls of the box. Find the interior area of the bottom of the box?

12. If the rate of inflation was 1000% then what will be the cost of an article two years from now, which costs 6 units of currency now?
A. 666
B. 660
C. 720
D. 726
E. 730

13. At a soccer match, the contractor provided dinner for 24 persons, and fixed the price so as to gain 12.5% upon his total outlay. Three of the players being absent , the remaining 21 paid the fixed price for their dinner, and such the contractor lost one rupee.
What was the charge for the dinner?

ORKUT QUANTDATABASE (Till Aug 5th)

7. If 'N' is the number of two digit numbers that are not the divisible by 7 and 5, then the value of n is?
A. 61
B. 83
C. 75
D. 56

10. If the median of a seven number sequence is 2n+2 then find the Arithmetic mean of that sequence?

11. If a number is divided by 24 and gives reminder as 21 then what is the divided of the following?
A. 6
B. 5
C. 3
D. 9
E. 21

ORKUT QUANTDATABASE (Till Aug 7th)

1. If standard deviation of 'p' number of people is 21.5 and standard deviation of 'q' number of people is 9 then what is that least possible standard deviation value when both p and q are added?
答：这道题我想了半天。感觉上是 sqrt[（21.5^2+9^2）/2]
但无法作答。请高手指点。

4. How many of the following 2, 4, -7, sqrt(19) & 8 have their square 4 more than the multiples of 5?
A. 0
B. 1
C. 2
D. 3
E. 4
答：4
题目的意思是说，2，4，-7，sqrt(19)和8平方后所得的数，有几个是5的整数倍+4（即被5整除余4）
2，-7，19，8的平方均可以表示成 5m+4


5. If A1, A2, A3, A4 & A5 belongs to a series such that An= n{(-1)^n -1}, then what will be the difference of the largest and the smallest term?
A. 4
B. 6
C. 8
D. 10
E. 12
答：D.
可以根据An的公式，看出来，n为偶数时，An=0；n为奇数时，均为负值；故可以看到A5的值最小为-10。

6. If R1 = -3,-2,-1
R2 = 1, 2, 3 &
R3 = -3, -2, -1, 1, 2, 3
and if s1, s2 ans s3 are standard deviations of R1, R2 and R3 then which of the following is true?
i. s1<S2
ii. s2<0
iii. s3=0

A. NONE
B. i only
C. ii only
D. iii only
E. all three
答：A
根据标准方差定义：S1=S2
R3序列的平均值为0，标准方差S3=sqrt(((-3)^2+(-2)^2+(-1)^2+1^2+2^2+3^2)/6)=sqrt(14/3)不为0

7. In a class of certain number of students, if 1/2 of the students takes maths as their major, 2/3 takes physics as their major & 1/3 takes both maths and physics as their majors and if 40 students didn't take any of maths or physics subjects as their major then what is the total number of students in the class?

8. If x < y then
Col A: x^2+x+1
Col B: y^2+y+1
答： D


12. Given a line in xy plane with slope k = -1/2
Col A: x-intercept
Col B: y-intercept
答：D

ORKUT QUANTDATABASE (Till Aug 6th)

1. What is the remainder of the following (7^0 + 7^1 + 7^2 + 7^3 + ........ + 7^23)/14 ?
答：8

8. A person went to market with a red and a green bag and bought 10 carrots & 6 radishes. On the way to home he distributed vegetables into the two bags in such a way that no bag is empty. In how many ways can he do ths?
答：75种
10个carrot没有区别，6个radish也没有区别
故10个carrot放到袋子里的方法（先不考虑其中一个袋子为空的情况），有11种方法。
同理，6个radish放入两个袋子的方法是7种
然后用乘法原则，7×11=77种。
只需排除2种情况，所有的萝卜们都放到了红袋子里或绿袋子里。
故77-2=75种。


9. In how many ways, the letters of the word POLLOLOP can be arranged?

10. If 60% children like cats, 70% like dogs and 80% like rabbits then exactly how many children like all three animals?
答：只知道至少有10%的孩子这三张动物都喜欢；至多就是60%。


11. A figure was given, it had a rectangular box in which 16 cylindrical cans, each with radius of 1 inch are placed. If the cans touch adjacent cans and/or the walls of the box. Find the interior area of the bottom of the box?
答：64 inch^2
用m个cylindrical can的直径× n个cylindrical can的直径即可
m和n分别为rectangular box的长边和宽边分别可以放的盒子的个数；无论取8，2或是16，1或4，4，答案都是一样

12. If the rate of inflation was 1000% then what will be the cost of an article two years from now, which costs 6 units of currency now?
A. 666
B. 660
C. 720
D. 726
E. 730
答案为 D
6(1+1000%)^2=726
(inflation rate 在Wiki百科上是指 “年通货膨胀率”)

13. At a soccer match, the contractor provided dinner for 24 persons, and fixed the price so as to gain 12.5% upon his total outlay. Three of the players being absent , the remaining 21 paid the fixed price for their dinner, and such the contractor lost one rupee.
What was the charge for the dinner?
答案为：3
设total outlay是x rupee, fixed price per person是 y rupee(卢布)
则 24y-x=12.5%*x
   21y-x=-1
根据上面两个方程，可得出：y=3 rupee


ORKUT QUANTDATABASE (Till Aug 5th)
7. If 'N' is the number of two digit numbers that are not the divisible by 7 and 5, then the value of n is?
A. 61
B. 83
C. 75
D. 56
答案是 B
因为：61=7×8+5
      75=5×15
      56=7×8
10. If the median of a seven number sequence is 2n+2 then find the Arithmetic mean of that sequence?
11. If a number is divided by 24 and gives reminder as 21 then what is the divided of the following?
A. 6
B. 5
C. 3
D. 9
E. 21
答案是 C
设此数为n，则n=24m+21(m为integer)  =>  n=m*3*2^3+3*7
故n可以被3整除。（“what is the divided of the following”：我理解为 “可被下面哪个数整除”）

倒数第二题好像选A吧，是在问到底有多少个两位数能够既不被7也不被5整除…