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gmat prep question

by yvonne12 » Sun Apr 29, 2007 1:58 pm
2^z - 2^z-3=224 what is the value of z??
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by Prasanna » Sun Apr 29, 2007 2:09 pm
2^z - 2^z-3=224

This means

2^z - 2^z/2^3=224

2^z-2^z/8=224

8(2^z)-2^z=224*8

7(2^z)=224*8

224*8=7*32*8=7*2^8

Hence z=8
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by Cybermusings » Mon Apr 30, 2007 1:00 am
2^z - 2^z-3=224

Taking 2^z-3 common
2^z-3 [ 2^3 - 1] = 224
2^z-3 [7] = 224
2^z-3 = 224/7 = 32
2^z-3 = 2^5
z-3 = 5
Hence z = 8
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