Please help with these problems

[Rapt0ria]

[skawal]

S=1-(1/2)+(1/3)-(1/4)+(1/5)-(1/6)+(1/7)-(1/8)+(1/9)-(1/10)
S=(1/2)+(1/3)-(1/4)+(1/5)-(1/6)+(1/7)-(1/8)+(1/9)-(1/10)
S=(1/2)[1+1/2 +1/3 +1/4 +1/5] +1/3 +1/5 +1/7+1/9

keep special eye to the bold terms.from the term you can see that this term [1+1/2 +1/3 +1/4 +1/5] is greater than 1 and 1/2 of these is greater than 1/2.if we add this number(greater than 1/2) with the another term [1/3 +1/5 +1/7+1/9] then we get a number that is also greater than 1/2.

so the ans is A.

for the first problem
1+2+3+4+5..........+47+48 separate it with the sum of the even integers and the odd integers.then we get

2+4+............+48 and 1+3+................47

no.of terms is = (24-1)+1=24 for both the cases.

sum of the even integers= [2*2 +(24-1)2]*24/2=300=V
sum of the even integers= [2*1 +(24-1)2]*24/2=288=D

so we can see that D+23 is greater than V.

For the last problem
72.42=k(24+ n/100) from the problem if k and n are positive integers and n is less than 100 you can easily make an assumption that k must me a number which is 3 to make balance of the equation that means 3*24 is equal to 72 and 3*(n/100) will give you .42

3*(n/100)=.42
so,n=14

so,k+n=14+3=17.

give me response whether im correct or not.

[Wiki]

Originally Posted by skawal

S=1-(1/2)+(1/3)-(1/4)+(1/5)-(1/6)+(1/7)-(1/8)+(1/9)-(1/10)
S=(1/2)+(1/3)-(1/4)+(1/5)-(1/6)+(1/7)-(1/8)+(1/9)-(1/10)
S=(1/2)[1+1/2 +1/3 +1/4 +1/5] +1/3 +1/5 +1/7+1/9

Confusing where did minus signs go?

Originally Posted by skawal

for the first problem
1+2+3+4+5..........+47+48 separate it with the sum of the even integers and the odd integers.then we get

2+4+............+48 and 1+3+................47

no.of terms is = (24-1)+1=24 for both the cases.

sum of the even integers= [2*2 +(24-1)2]*24/2=300=V
sum of the even integers= [2*1 +(24-1)2]*24/2=288=D

so we can see that D+23 is greater than V.

Sum of even and odd integers is wrong,
Correct values are:
V = 600
D = 576

D + 23 = 599

V is greater

Originally Posted by skawal

For the last problem
72.42=k(24+ n/100) from the problem if k and n are positive integers and n is less than 100 you can easily make an assumption that k must me a number which is 3 to make balance of the equation that means 3*24 is equal to 72 and 3*(n/100) will give you .42

3*(n/100)=.42
so,n=14

so,k+n=14+3=17.

Correct

[Wiki]

Question#1

25% of 80 = 20

Reduced total = 75

What percent is 20 of 75?

%x= 20*100/75 = 26.666% approximaltely 27%

[skawal]

wiki,thanks for infoming me my mistakes.for the first problem i accept my error.but for the second problem, it was a typo.

[skawal]

for the combination problem,i dont know whether my reasoning is correct or not.however,below my reasoning.

if 2 integers is selected from 10 integers there should be 45 possible selections.

the question asked you to select the possible selections that consists of one odd and one even integer.

selection consists of only even integers=5c2=10
selection consists of only odd integers=5c2=10

so possible selections that consists of one odd and one even integer
=45-(10+10)=25

[aimgre08]

yes that is correct for that combination problem and

for the other combination problem on dollars,(am not sure if i am correct!!)
Total no of ways of giving 7 dollars to 3 people and each should have min.1 dollar is similar to no. of ways of giving 4 dollars to 3 people = 3^4

Total no. of ways of giving 7 dollsrs to 3 people and 1 getting min 3dollars, other two a minimum of 1 dollar is similar to no of ways of giving 2 dollars to 3 people = 3^2

so the value in Column B is greater.

[gre320hex]

Originally Posted by skawal

S=1-(1/2)+(1/3)-(1/4)+(1/5)-(1/6)+(1/7)-(1/8)+(1/9)-(1/10)
S=(1/2)+(1/3)-(1/4)+(1/5)-(1/6)+(1/7)-(1/8)+(1/9)-(1/10)
S=(1/2)[1+1/2 +1/3 +1/4 +1/5] +1/3 +1/5 +1/7+1/9

keep special eye to the bold terms.from the term you can see that this term [1+1/2 +1/3 +1/4 +1/5] is greater than 1 and 1/2 of these is greater than 1/2.if we add this number(greater than 1/2) with the another term [1/3 +1/5 +1/7+1/9] then we get a number that is also greater than 1/2.

so the ans is A.

for the first problem
1+2+3+4+5..........+47+48 separate it with the sum of the even integers and the odd integers.then we get

2+4+............+48 and 1+3+................47

no.of terms is = (24-1)+1=24 for both the cases.

sum of the even integers= [2*2 +(24-1)2]*24/2=300=V
sum of the even integers= [2*1 +(24-1)2]*24/2=288=D

so we can see that D+23 is greater than V.

For the last problem
72.42=k(24+ n/100) from the problem if k and n are positive integers and n is less than 100 you can easily make an assumption that k must me a number which is 3 to make balance of the equation that means 3*24 is equal to 72 and 3*(n/100) will give you .42

3*(n/100)=.42
so,n=14

so,k+n=14+3=17.

give me response whether im correct or not.

Actually, I read a better way to answer this kind of a question elsewhere. Notice, that every time a greater term is getting added than the term that is being subtracted. And, we see that the first 2 terms are 1-1/2= 12/. From, after that we have 1/2 + ( 1/2-1/4+1/5..) ie. 1/2 + ( bigger term - smaller term ). Therefore, S is greater than 1/2

[skawal]

for aimgre,the ans for the dollar problem is C.when i took exam in the powerprep i got the problem.i also posted the problem here but i have the confusion yet.

[skawal]

Originally Posted by gre320hex

Actually, I read a better way to answer this kind of a question elsewhere. Notice, that every time a greater term is getting subtracted than the term that is being added. And, we see that the first 2 terms are 1-1/2. Therefore, S can never be more than 1/2. Hence, S < 1/2 . The answer needs to be B

according to your reasoning should the ans be A?