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.
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
can somebody explain these problems
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- shovan85
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Please follow the below link for detailed explanation:
https://www.beatthegmat.com/easy-but-tricky-t68043.html
- shovan85
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IMO Dhassasin wrote: 3. If k is a positive integer, then 20k is divisible how many different positive integers ?
(1) k is prime
(2) k=7
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)
- shovan85
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Please check the options. Something is missing it seemshassasin 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)
- shovan85
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IMO Dhassasin 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.
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.
i am sorry the options should be equal to zeroshovan85 wrote:Please check the options. Something is missing it seemshassasin 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
- Fatehdeep Singh
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shovan85 wrote:IMO Dhassasin wrote: 3. If k is a positive integer, then 20k is divisible how many different positive integers ?
(1) k is prime
(2) k=7
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!!!
- shovan85
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Agreed!! My mistakeFatehdeep Singh wrote:shovan85 wrote:IMO Dhassasin wrote: 3. If k is a positive integer, then 20k is divisible how many different positive integers ?
(1) k is prime
(2) k=7
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.
If the problem is Easy Respect it, if the problem is tough Attack it
shouldn,t C = kTL^2 since lenght is directly proportional and not inversely proportionalshovan85 wrote:IMO Dhassasin 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.
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.
- shovan85
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Yes!! Sorry I read it Inversely proportional...hassasin wrote: shouldn,t C = kTL^2 since lenght is directly proportional and not inversely proportional
Anyways as it is a Data Sufficiency it will not harm our Answer
If the problem is Easy Respect it, if the problem is tough Attack it
- Geva@EconomistGMAT
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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?"hassasin wrote:i am sorry the options should be equal to zeroshovan85 wrote:Please check the options. Something is missing it seemshassasin 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
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]