Problem Solving

Please help with these questions form GMATPrep 1, which i got wrong. If any of these questions were discussed earlier please give the link. Will post OAs later.

1. For every positive integer n, the function h(n) is defined to be product of all even integers form 2 to n, inclusive. If p is the smallest prime factor of h(100)+1, then p is

A. between 2 and 10
B. between 10 and 20
C. between 20 and 30
D. between 30 and 40
E. greater than 40


2. The number of stamps Kaye and Alberto had were in the ration 5:3 respectively . After Kaye gave Alberto 10 of her stamps , the ratio of the number of stamps Kaye had to number Alberto had was 7:5. As a result of this gift, Kaye had how many more stamps than Alberto?

A. 20
B. 30
C. 40
D. 60
E. 90

In my calculations I am getting 60, but this is not correct.

3. At a certain university , the ratioof the number of teachers to number of students in any course must always be greater than 3:80. What is the maximum number of students possible in a course that has 5 teachers?

A. 130
B. 131
C. 132
D. 133
E. 134

bkobilov wrote:Please help with these questions form GMATPrep 1, which i got wrong. If any of these questions were discussed earlier please give the link. Will post OAs later.

3. At a certain university , the ratioof the number of teachers to number of students in any course must always be greater than 3:80. What is the maximum number of students possible in a course that has 5 teachers?

A. 130
B. 131
C. 132
D. 133
E. 134

D
3/80 < T/S
We know T = 5,
So, 3/80 = 5/S
3S < 400
S < 133.33
So, S the max number of students is 133.

1. For every positive integer n, the function h(n) is defined to be product of all even integers form 2 to n, inclusive. If p is the smallest prime factor of h(100)+1, then p is

A. between 2 and 10
B. between 10 and 20
C. between 20 and 30
D. between 30 and 40
E. greater than 40

IMO (A).

since the function involves the product of all even integers from 2 to n inclusive

h(100)+1 = an odd number. for h(100) alone the smallest prime factor would be 2.

so for h(100)+1, I think the smallest prime factor = 3. Since in the multiplication of the function, the number will include 12 as one of the integers being multiplied. 12 is divisible by 3. So any number multiplied by 12 is also divisible by 3.

Hence (a)

bkobilov wrote:Please help with these questions form GMATPrep 1, which i got wrong. If any of these questions were discussed earlier please give the link. Will post OAs later.

2. The number of stamps Kaye and Alberto had were in the ration 5:3 respectively . After Kaye gave Alberto 10 of her stamps , the ratio of the number of stamps Kaye had to number Alberto had was 7:5. As a result of this gift, Kaye had how many more stamps than Alberto?

A. 20
B. 30
C. 40
D. 60
E. 90

In my calculations I am getting 60, but this is not correct.

I believe what you are doing is solving for K and A, and getting 150 - 90 = 60 and marking that as the answer. I did the exact same thing, but for me I came up with the right answer knowing 60 isnt the answer (thanks to your comment).
Read the part highlighted in red above. The question asks the value of (K-10) - (A+10), which will give you (150-10) - (90+10) = 140-100 = 40.
Pick C.

1. For every positive integer n, the function h(n) is defined to be product of all even integers form 2 to n, inclusive. If p is the smallest prime factor of h(100)+1, then p is

A. between 2 and 10
B. between 10 and 20
C. between 20 and 30
D. between 30 and 40
E. greater than 40

this one is E
h(100) = 2 * 3 * 4.............................*100 = 2( 1*2*.................*50) so h(100) is divisible by all primes below 50 ...Hence h(100) +1 will leave a remainder of 1 when divided by any prime from 2 to 47... So the smallest prime which divides h(100) +1 has to be greater than 47 ...... Hence option E

2. The number of stamps Kaye and Alberto had were in the ration 5:3 respectively . After Kaye gave Alberto 10 of her stamps , the ratio of the number of stamps Kaye had to number Alberto had was 7:5. As a result of this gift, Kaye had how many more stamps than Alberto?

A. 20
B. 30
C. 40
D. 60
E. 90

In my calculations I am getting 60, but this is not correct.

Kaye : Alberto (5/8)x: (3/8)x if x is the total number of stamps
Now Kaye gives alberto 10 stamps

(5/8)x- 10 : (3/8)x + 10 = 7/5
(25/8)x - 50 = (21/8)x + 70
(4/8)x = 120
x = 240

Kaye has (5/8)x- 10 - [(3/8)x + 10] more stamps
= (2/8)X -20 = 60 -20 =40 stamps

2. The number of stamps Kaye and Alberto had were in the ration 5:3 respectively . After Kaye gave Alberto 10 of her stamps , the ratio of the number of stamps Kaye had to number Alberto had was 7:5. As a result of this gift, Kaye had how many more stamps than Alberto?

A. 20
B. 30
C. 40
D. 60
E. 90


Answer

5x-10 / 3x+10 = 7/5
25x - 50 = 21x+70
4x = 120
x = 30

Kaye = 140
Alberto = 100

Kaye has 40 stamps more.

Hence the answer is (C) i.e.40.

3. At a certain university , the ratioof the number of teachers to number of students in any course must always be greater than 3:80. What is the maximum number of students possible in a course that has 5 teachers?

A. 130
B. 131
C. 132
D. 133
E. 134

Answer:

T / s > 3/80

=> 5/s > 3/80
=> 3s<400
=> s<133.33

The closest one is option (D) i.e. 133