GMAT Problem Solving Discussions

MBA
2357
PLZ help me in this question..
If k, m, and t are positive integers and + = , do t and 12 have a common factor greater than 1 ?
(1) k is a multiple of 3.
(2) m is a multiple of 3.


Plz explain the highlighted section...
2358

Hi,
Does anyone have Manhattan prep guide for Geometry and Equalities/Inequalities to share? Or can direct me where to find them?
Many thanks in advance,
-Ravi

2359
Hi,
Does anyone have Manhattan prep guide for Geometry and Equalities/Inequalities to share? Or can direct me where to find them?
Many thanks in advance,
-Ravi



Ravi,

If you are looking for a non-genuine copy of these books....you are looking at the wrong place. We are bound by sound ethics here on PG, and cannot share anything that is not legal.

Otherwise, Check:

Amazon.com: Geometry GMAT Preparation Guide (Manhattan GMAT Preparation Guides): Books
Amazon.com: Equations, Inequalities, and VIC's, GMAT Preparation Guide, 4th Edition (Manhattan GMAT Preparation Guides): Manhattan GMAT Prep: Books
GMAT Strategy Guides & Online Resources GMAT Store ManhattanGMAT

Good Luck,
Vikram
2360

Thanks Vikram,
I welcome all versions of the Manhattan prep guides. Amazon appears to have some good deals.

Thanks
rpm

2361

Joey had a rectangular tank with a lid made of metallic sheet to store water. The length, breadth and ht of the tank measured 6, 3, 4 feet respectively. He wanted to maximize the quantity of water that he could store. So he got a new tank made using sheet having the same surface area. How much more water was he able to store approx?

2362

A semi-circular paper of negligible thickness having a radius of 4 units is made into a rt circular cone with negligible wastage. What is the ht of the rt circular cone?

2363

A quick one Puys...

2(raised to power a) + 3(raised to power b) = 35
2(raised to power a +3) - 3(raised to power b + 1) = 49

find a & b?

2364
friend9921 Says
Joey had a rectangular tank with a lid made of metallic sheet to store water. The length, breadth and ht of the tank measured 6, 3, 4 feet respectively. He wanted to maximize the quantity of water that he could store. So he got a new tank made using sheet having the same surface area. How much more water was he able to store approx?

Of all the shapes having same surface area, the volume of sphere is maximum.

Surface Area of Sphere = Surface Area of cuboidal tank
= 2(6*3 + 3*4 + 6*4) = 2*54 = 108
so 4 pi r^2 = 108
i.e. r = 3 (3/pi)^1/2
So, v= 4/3pi r^3 = 108 (3/pi)^1/2 = 105.6 cubic feet

so increase in volume = 105.6 - 72 = 33.6 cubic feet
2365

Thank you amar. I understood the solution, but i still have a doubt.

So, v= 4/3pi r^3 = 108 (3/pi)^1/2 = 105.6 cubic feet

How did calculate (3/pi)^1/2.

Logically i understood 3/pi gives you 0.95 and the root of it gives u 0.977; which further gives you the ans.

I am just asking how did you calculate the root of 0.977???

I had to use a calci for the same.


Of all the shapes having same surface area, the volume of sphere is maximum.

Surface Area of Sphere = Surface Area of cuboidal tank
= 2(6*3 + 3*4 + 6*4) = 2*54 = 108
so 4 pi r^2 = 108
i.e. r = 3 (3/pi)^1/2
So, v= 4/3pi r^3 = 108 (3/pi)^1/2 = 105.6 cubic feet

so increase in volume = 105.6 - 72 = 33.6 cubic feet
2366
Thank you amar. I understood the solution, but i still have a doubt.

So, v= 4/3pi r^3 = 108 (3/pi)^1/2 = 105.6 cubic feet

How did calculate (3/pi)^1/2.

Logically i understood 3/pi gives you 0.95 and the root of it gives u 0.977; which further gives you the ans.

I am just asking how did you calculate the root of 0.977???

I had to use a calci for the same.


Hey buddy ...
Degree of approximation would depend on how close are the answer options ...And very rarely on GMAT, would the ans options be so close that exact value of root 0.977 really matter ...its too close to 1 ...we can approx it to 1 ...

For that matter, we can approx pi as 3 and avoid calculations ...so if we take pi as 3 ...volume is 108 ..i doubt we would have more than 1 option between 105.6 and 108 .....
2367
A quick one Puys...

2(raised to power a) + 3(raised to power b) = 35
2(raised to power a +3) - 3(raised to power b + 1) = 49

find a & b?


I think there is a misprint or typo in here.. it should be;

2(raised to power a) + 3(raised to power b) = 35
2(raised to power a +2) - 3(raised to power b + 1) = -49
..
OR
..
2(raised to power a) + 3(raised to power b) = 35
2(raised to power a +4) - 3(raised to power b + 1) = 47

Also, I am assuming both a and b are integers ;)
so the answer would be, a=3 and b=3.






NOTE: If my assumptions dont hold good.. then neither do my answers
2368
Thank you amar. I understood the solution, but i still have a doubt.

So, v= 4/3pi r^3 = 108 (3/pi)^1/2 = 105.6 cubic feet

How did calculate (3/pi)^1/2.

Logically i understood 3/pi gives you 0.95 and the root of it gives u 0.977; which further gives you the ans.

I am just asking how did you calculate the root of 0.977???

I had to use a calci for the same.


Finding a square root doesnt take much time. And yes you can always approximate the value. Just by looking you can see that square root of 95 will be greater than 9 and less than 10.
2369
A quick one Puys...

2(raised to power a) + 3(raised to power b) = 35
2(raised to power a +3) - 3(raised to power b + 1) = 49

find a & b?


If indeed what varun has assumed is not true , solution does not feel like a GMAT soln, it involves logs !!

2^a + 3^b =35 ....(1)

2^(a+3) - 3(b+1) =49
i.e 8*2^a - 3*3^b = 49 ....(2)

sub value of 2^a from (1) in (2)
Hence,
8(35-3^b) - 3*3^b = 49

so, 11*3^b = 231 ...i.e 3^b = 21
And 2^a =14

So wierd looking ans turn out to be ..
a = log 14 (to the base 2)
b = log 21 (to the base 3)

P.S : I doubt the question ..
2370
A quick one Puys...

2(raised to power a) + 3(raised to power b) = 35
2(raised to power a +3) - 3(raised to power b + 1) = 49

find a & b?

we get 2^a=14 and 3^b=21

so this means that a,b are real and cannot be integers.

Need more info on a&b; or at least give answer choices.
2371
A quick one Puys...

2(raised to power a) + 3(raised to power b) = 35
2(raised to power a +3) - 3(raised to power b + 1) = 49

find a & b?


let 2^a=x and 3^b=y
x+y=35
8x-3y=49
after solving-
x=14 and y=21

2^a=14
approx value of a=3.5
3^b=21 , approx value of b =2.5 taking mid values.
2372
friend9921 Says
A semi-circular paper of negligible thickness having a radius of 4 units is made into a rt circular cone with negligible wastage. What is the ht of the rt circular cone?


is the answer 4?
2373
guy with guts Says
is the answer 4?


My answer:-2*root(3)
2374
friend9921 Says
A semi-circular paper of negligible thickness having a radius of 4 units is made into a rt circular cone with negligible wastage. What is the ht of the rt circular cone?


Conservation of TSA=>
TSA=pi*r1*l=1/2*pi*r2^2=>2*r1*l=r2^2=16
=>sqrt(l^2-h^2)*l=8=4x2=>
l=4=>h^2=16-4=>h=2*sqrt2=2*1.414=2.828(approx).
2375
friend9921 Says
A semi-circular paper of negligible thickness having a radius of 4 units is made into a rt circular cone with negligible wastage. What is the ht of the rt circular cone?



The radius of the circle will form the slant height of the cone.
So, slant height,s =4 units
The semi- circumference of circle will be the circumference of the cone.
Let the radius of the cone be R and that of circle =r.
Then, pi*r=2*pi*R
Since r=4;R=2.
Now we know slant height of cone=sqrt(radius^2+height^2)
=>4=sqrt(2^2+h^2)
=>h=sqrt(12)=2*sqrt(3)
2376

thanks for the quickreply mates!
there indeed is a misprint in the Ques... and the 1st option suggested by NuttyVarun is the right one

cheers