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can somebody explain these problems

by hassasin » Sun Oct 17, 2010 10:30 am
1. The cost of a square slab is proportional to its thickness and also proportional to the square of its length. What is the cost of a square slab that is 3 meters long and 0.1 meter thick ?

(1) The cost of a square slab that is 2 meter long ans 0.2 meter thick is $160 more than the cost of a square slab that is 2 meters long and 0.1 meter thick.
(2) The cost of a square slab that is 3 meter long and 0.1 meter thick is $200 more than the cost of a square slab that is 2 meters long and 0.1 meter thick.

2. In the x-y plane, does the line with the equation y=3x+2 contain the point (r,s) ?

(1) (3r+2-s)(4r+9-s)= 0
(2) (4r-6-s)(3r+2-s)= 0

3. If k is a positive integer, then 20k is divisible how many different positive integers ?

(1) k is prime
(2) k=7

4.
Image

On the number line shown,is zero half way between r and s
(1) s is to the right of the zero
(2) The distance between t and r is the same as the distance between t and -s
Last edited by hassasin on Sun Oct 17, 2010 8:58 pm, edited 1 time in total.
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by shovan85 » Sun Oct 17, 2010 10:54 am
hassasin wrote: 4.
Image

On the number line shown,is zero half way between r and s
(1) s is to the right of the zero
(2) The distance between t and r is the same as the distance between t and -s
Please follow the below link for detailed explanation:
https://www.beatthegmat.com/easy-but-tricky-t68043.html
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by shovan85 » Sun Oct 17, 2010 11:07 am
hassasin wrote: 3. If k is a positive integer, then 20k is divisible how many different positive integers ?

(1) k is prime
(2) k=7
IMO D

2: 20k = 140 = 2^2 * 5^1 * 7 ^ 1
Total positive divisors = (2+1)(1+1)(1+1) = 12 (Not required step but Sufficient)

1: k is prime that means k has no other divisors but 1 and k.
20K = 2^2* 5^1 * k^1 (as k is prime)
Total positive divisors = (2+1)(1+1)(1+1) = 12 (Not required step but Sufficient)
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by shovan85 » Sun Oct 17, 2010 11:11 am
hassasin wrote: 2. In the x-y plane, does the line with the equation y=3x+2 contain the point (r,s) ?

(1) (3r+2-s)(4r+9-s)
(2) (4r-6-s)(3r+2-s)
Please check the options. Something is missing it seems :(
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by shovan85 » Sun Oct 17, 2010 11:22 am
hassasin wrote:1. The cost of a square slab is proportional to its thickness and also proportional to the square of its length. What is the cost of a square slab that is 3 meters long and 0.1 meter thick ?

(1) The cost of a square slab that is 2 meter long ans 0.2 meter thick is $160 more than the cost of a square slab that is 2 meters long and 0.1 meter thick.
(2) The cost of a square slab that is 3 meter long and 0.1 meter thick is $200 more than the cost of a square slab that is 2 meters long and 0.1 meter thick.
IMO D

C = kT/L^2 (C = Cost, k = proportionality constant, T= thickness, L=length ) .....[a]

1:
C' = k(0.2)/(2^2) = 0.05k
C" = k(0.1)/(2^2) = 0.025k

Thus C' - C" = 160
=> 0.025k = 160

So k is found and thus C can be found by putting the values in [a]

2: Information is exact except the data. But still the same way solvable.
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by hassasin » Sun Oct 17, 2010 8:57 pm
shovan85 wrote:
hassasin wrote: 2. In the x-y plane, does the line with the equation y=3x+2 contain the point (r,s) ?

(1) (3r+2-s)(4r+9-s)=0
(2) (4r-6-s)(3r+2-s)=0
Please check the options. Something is missing it seems :(
i am sorry the options should be equal to zero
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by Fatehdeep Singh » Sun Oct 17, 2010 10:16 pm
shovan85 wrote:
hassasin wrote: 3. If k is a positive integer, then 20k is divisible how many different positive integers ?

(1) k is prime
(2) k=7
IMO D

2: 20k = 140 = 2^2 * 5^1 * 7 ^ 1
Total positive divisors = (2+1)(1+1)(1+1) = 12 (Not required step but Sufficient)

1: k is prime that means k has no other divisors but 1 and k.
20K = 2^2* 5^1 * k^1 (as k is prime)
Total positive divisors = (2+1)(1+1)(1+1) = 12 (Not required step but Sufficient)

I do not think 1 is sufficient

Lets see why
Case I: K is prime other than 2 & 5 (say 7,11,13)
Then no of factors:
20*7 = 2^2 * 5^1 *7^1=(2+1)(1+1)(1+1) = 12

Case II: K is 2
No of factors:
20*2 = 2^3 *5 = (3+1)(1+1) =8

Case III: K is 5
No of factors:
20*5 = 2^2 * 5^2 =(2+1)(2+1)=9

Hence no definite value.So not sufficient.
Deg Teg Fateh!!!
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by shovan85 » Mon Oct 18, 2010 2:21 am
Fatehdeep Singh wrote:
shovan85 wrote:
hassasin wrote: 3. If k is a positive integer, then 20k is divisible how many different positive integers ?

(1) k is prime
(2) k=7
IMO D

2: 20k = 140 = 2^2 * 5^1 * 7 ^ 1
Total positive divisors = (2+1)(1+1)(1+1) = 12 (Not required step but Sufficient)

1: k is prime that means k has no other divisors but 1 and k.
20K = 2^2* 5^1 * k^1 (as k is prime)
Total positive divisors = (2+1)(1+1)(1+1) = 12 (Not required step but Sufficient)

I do not think 1 is sufficient

Lets see why
Case I: K is prime other than 2 & 5 (say 7,11,13)
Then no of factors:
20*7 = 2^2 * 5^1 *7^1=(2+1)(1+1)(1+1) = 12

Case II: K is 2
No of factors:
20*2 = 2^3 *5 = (3+1)(1+1) =8

Case III: K is 5
No of factors:
20*5 = 2^2 * 5^2 =(2+1)(2+1)=9

Hence no definite value.So not sufficient.
Agreed!! My mistake :(
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by hassasin » Mon Oct 18, 2010 2:29 am
shovan85 wrote:
hassasin wrote:1. The cost of a square slab is proportional to its thickness and also proportional to the square of its length. What is the cost of a square slab that is 3 meters long and 0.1 meter thick ?

(1) The cost of a square slab that is 2 meter long ans 0.2 meter thick is $160 more than the cost of a square slab that is 2 meters long and 0.1 meter thick.
(2) The cost of a square slab that is 3 meter long and 0.1 meter thick is $200 more than the cost of a square slab that is 2 meters long and 0.1 meter thick.
IMO D

C = kT/L^2 (C = Cost, k = proportionality constant, T= thickness, L=length ) .....[a]

1:
C' = k(0.2)/(2^2) = 0.05k
C" = k(0.1)/(2^2) = 0.025k

Thus C' - C" = 160
=> 0.025k = 160

So k is found and thus C can be found by putting the values in [a]

2: Information is exact except the data. But still the same way solvable.
shouldn,t C = kTL^2 since lenght is directly proportional and not inversely proportional
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by shovan85 » Mon Oct 18, 2010 2:36 am
hassasin wrote: shouldn,t C = kTL^2 since lenght is directly proportional and not inversely proportional
Yes!! Sorry I read it Inversely proportional...
Anyways as it is a Data Sufficiency it will not harm our Answer
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by Geva@EconomistGMAT » Mon Oct 18, 2010 5:31 am
hassasin wrote:
shovan85 wrote:
hassasin wrote: 2. In the x-y plane, does the line with the equation y=3x+2 contain the point (r,s) ?

(1) (3r+2-s)(4r+9-s)=0
(2) (4r-6-s)(3r+2-s)=0
Please check the options. Something is missing it seems :(
i am sorry the options should be equal to zero
Translate the question: when asking "does the line y=3x+2 contain the point (r,s)?" the question is really asking "do r and s maintain this relationship between each other?" In other words, "is s=3r+2?"

According to stat. (1), either 3r+2-s=0 Or 4r+9-s=0
In the first case, s=3r+s, so the point r,s satisfies the equation y=3x+2 and the answer is yes.
In the second case, s=4r+9, so the point r,s does not satisfy the equation y=3x+2 and the answer is no.
Insufficient.

Stat. (2): perform the same analysis:
If 4r-6-s=0, then s=4r-6 and the answer is no.
If 3r+s-s=0, then s=3r+2 and the answer is yes.
Insufficient.

combined, only s=3r+2 satisfies both statements, as each statement eliminates the alternative scenario from the other statement:
According to stat. (1), 4r+9-s could equal 0, but then the expression in stat. (2) will not equal 0, so this scenario is eliminated by stat. (2)
And the same goes for stat. (2)s 4r-6-s=0, which does not satisfy stat. (1).

so the answer to the question "is s=3r+2 is a definite "yes". [/list]
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