# Thread: How many positive integers can be expressed as a product...

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## How many positive integers can be expressed as a product...

• How many positive integers can be expressed as a product of 2 or more of the prime numbers 5,7,11,13 if no one product is to use the same prime number more than once ?
· 8

· 9

· 10

· 11

· 12

Ans - 11

• If 72.42 = k (24 + n/100), k and n are positive integers, n < 100, then k + n =?
· 17

· 16

· 15

· 14

· 13

Ans – 17

• S = 1 –1/2+ 1/3 – 1/4 + 1/5 –1/6 +1/7-1/8+1/9-1/10

A B

S 0.5

Ans – A

• It takes 60 sq tiles,2 feet on each side to cover a certain rectangular floor completely, without overlap.

A B

(No of sq tiles,1 foot on each side that 120

It would take to completely cover floor, no overlap)

Ans - A

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1.Take all possible combinations:
5*7, 5*7*11 , 5*7*13 , 5*7*11*13 , 7*11 , 7*13, 11*5 , 11*13 , 13*5 , 13*5*11 , 13*7*11

Totally 11.

2.Dunno

3.Considering the 1st 2 terms,S=1-1/2 gives you 0.5 ... So, with that lets calculate the rest...
Group the terms, (1/3-1/4)+(1/5-1/6)+(1/7-1/8)+(1/9-1/10)
So,by LCM , we get 1/12 + 1/30 + 1/56 + 1/90 ..... All are positive terms that give rise to a positive number for sure..

So, obviously 0.5+ (positive term) will give answer greater than 0.5

4. Area= a*a
A. Area=2*2=4
60 sq tiles =60*4=240 sq.feet is the area(not overlapped)
B. Area=1*1=1
120 sq tiles=120*1 =120 sq.feet is the area(not overlapped)

A has greater area
So answer is A. I m a bit doubtful with this answer...

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## hi

You got all of them rite except second problem ....wow!! keep it up ..hope you ace the same way in your test. When is your test ??

4. Good post? |
Thanks a lot. I m taking the test on October 24. It feels good when i get these answers right although i didn't have any idea on the 2nd question.
I would like to know the answer for the 2nd question.
Thanks

5. Good post? |
answer for 2nd prob =17..good luck !!

6. Good post? |

## solution for prob2

If 72.42=k[24+(n/100)] and if n and k are positive integers, then k+n=?

17

16

15

14

13
72.42 = 24k + nk/100
72 + 42/100 = 24k + nk/100

72 = 24k ....... k = 3
42 = nk ......... n = 14
n + k = 17

7. Good post? |
1) 4C4 + 4C3 + 4C2 = 1+4+6 = 11

2) 72.42 = k(24+n/100) = 24k + nk/100
=> 7242 = 2400k + nk
=> 7242/k = 2400+n
2400*4 = 9600 > 7242 so k<=3 (k=1|2|3)
=> 7242/k = 7242|3621|2414
since n<100 then 2400+n < 2500
this leaves only 2414 with k=3, n=14 and n+k=17

3) Explanation by mission man is excellent.

4) Area of a single 2-by-2 tile = 4 sq.feet.
Floor area = 60*4 = 240 sq.feet.
Area of a single 1-by-1 tile = 1 sq.feet.
Number of such tiles required for covering the floor = 240/1 = 240 > 120 (A).

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