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5^21 * 4^11 = 2 * 10^n
LHS :
5^21 * 4^11
= 5^21 * 2 * 2* 4^10
= 5^21 * 2 * 2* (2*2)^10
= 5^21 * 2 * 2* 2^10 *2^10
= 5^21 * 2 * 2^21
= 2* 5^21* 2^21
= 2* 10^21 ==> n =21
- by nithi_mystics
Wed Sep 22, 2010 7:46 am- Forum: Problem Solving
- Topic: GmatPrep1
- Replies: 1
- Views: 832
- by nithi_mystics
Wed Sep 22, 2010 7:23 am- Forum: Problem Solving
- Topic: GmatPrep2
- Replies: 1
- Views: 926
- by nithi_mystics
Wed Sep 22, 2010 7:22 am- Forum: Problem Solving
- Topic: GmatPrep3
- Replies: 1
- Views: 1333
Greatest possible number of households that have all three of these devices = 55 (since that's the smallest of the numbers 80,75 and 55) Lowest possible number of households that have all three of these devices = 10 So, x-y = 45. Pls check the thread mentioned below to find the lowest possible numbe...
- by nithi_mystics
Sat Aug 14, 2010 5:14 am- Forum: Problem Solving
- Topic: all three of these devices
- Replies: 1
- Views: 933
My bad!! :( This is true that we can add/subtract similar inequalities -2 < a < 11 3 < b < 12 Added 1 < a + b < 23 , A true D true; eliminated I think this is incorrect. -2 < a < 11 ==> a can have values -1,1,0...10 3 < b < 12 ===> b can have values 4,5,6...11 So a+b can have the values 3,4...22 ==>...
- by nithi_mystics
Fri Aug 13, 2010 12:36 pm- Forum: Problem Solving
- Topic: Problem on inequalities
- Replies: 9
- Views: 1746
This is true that we can add/subtract similar inequalities -2 < a < 11 3 < b < 12 Added 1 < a + b < 23 , A true D true; eliminated I think this is incorrect. -2 < a < 11 ==> a can have values -1,1,0...10 3 < b < 12 ===> b can have values 4,5,6...11 So a+b can have the values 3,4...22 ==> 2 < a+b < ...
- by nithi_mystics
Fri Aug 13, 2010 11:37 am- Forum: Problem Solving
- Topic: Problem on inequalities
- Replies: 9
- Views: 1746
x+y = a
x^2 + y^2 + 2xy = a^2
Similarly, x^2 + y^2 - 2xy = b^2
a^2 - b^2 = 4xy
==> 2xy = (a^2 - b^2)/2
- by nithi_mystics
Thu Aug 12, 2010 3:03 pm- Forum: Problem Solving
- Topic: How do I do this
- Replies: 2
- Views: 1044
Total time taken = 840/60 = 14 hours. The train reached Chicago at 6 PM. So it should have started Newyork at 4 AM (Chicago time) ie., 5 AM NewYork time. <1>A train travels from New York City to Chicago, a distance of approximately 840 miles, at an average rate of 60 miles per hour and arrives in Ch...
- by nithi_mystics
Wed Aug 11, 2010 1:48 pm- Forum: Problem Solving
- Topic: Problem Solving
- Replies: 3
- Views: 1189
It was trial and error method. Since we want the max value, I did not chose 1 for x,y or z. Similarly no 0. So we are left with the numbers, 2,3,4,5,6,7,8 If we take 3 numbers that add up to 12 (say 4,6,2), we would assign the highest value to y(since the term has y^3), the second highest value to x...
- by nithi_mystics
Sun Aug 08, 2010 4:19 am- Forum: Problem Solving
- Topic: Maximum value of an expression
- Replies: 7
- Views: 1436
Answer is C.
Stmt 1 : INSUFF because values of a and b cannot be determined
Stmt 2 : INSUFF - same as above
From the 2 statements,
2b+6 = 3b
==> b = 6
and a=18. GCD is 6.
gmatrant wrote:If a and b are positive integers divisible by 6, is 6 the greatest common divisor of a and b?
I. a = 2b+6
II.a =3b
- by nithi_mystics
Fri Aug 06, 2010 5:58 pm- Forum: Problem Solving
- Topic: Is 6 the GCD of a & b
- Replies: 1
- Views: 1032
Stuart, have a doubt here. Can't we chose the same vowel twice. Like 'eed' or 'aaf' or have 'aaa', 'eee', 'aae' etc ? Shouldn't this be considered too? The number of words that can be formed out of the letters a,b,c,d,e,f taken 3 together each word containing atleast one vowel. a)96 b)90 c)24 d)120 ...
- by nithi_mystics
Fri Aug 06, 2010 5:49 pm- Forum: Problem Solving
- Topic: Problem on permutation & combination
- Replies: 5
- Views: 1196
- by nithi_mystics
Fri Aug 06, 2010 5:43 pm- Forum: Problem Solving
- Topic: Range of squares - Set
- Replies: 4
- Views: 1113
- by nithi_mystics
Fri Aug 06, 2010 12:34 pm- Forum: Problem Solving
- Topic: Maximum value of an expression
- Replies: 7
- Views: 1436
Guys, you are wrong. x+y should be <-1 and not <=-1 It is given that x+y+z>0 and we have to find if z>0 ie.. the minimum value of z = 1. Now if z = 1, x+y cannot be -1. It has to be less than -1 (only then x+y+z will be greater than 0) Therefore, z>0 can be rephrased as x+y <-1 I think its should be...
- by nithi_mystics
Fri Aug 06, 2010 8:15 am- Forum: Problem Solving
- Topic: DS Rephrasing / Number Props problem
- Replies: 19
- Views: 3097
The second statement is
x+y+1 < 0
Adding -1 to both sides,
x+y+1-1 < -1
===> x+y < -1
missrochelle wrote:selango wrote:
The question rephrased is such a way that we are taking x+y as negative and z as positive.
.
Why are we taking x+y as negative? I think that's where I am getting hung up.
- by nithi_mystics
Fri Aug 06, 2010 7:12 am- Forum: Problem Solving
- Topic: DS Rephrasing / Number Props problem
- Replies: 19
- Views: 3097