Vincen wrote: ↑Wed Jul 22, 2020 12:54 pm
How many digits are there in the product \(2^{23}\cdot 5^{24}\cdot 7^3?\)
A. 24
B. 25
C. 26
D. 27
E. 28
[spoiler]OA=D[/spoiler]
Source: Veritas Prep
Looking at \(2^{23}\cdot 5^{24}\cdot 7^3,\) we find that there are 2s and 5s; a 2 and a 5 make a 10. Since there are 23 2s and 24 5s, the product of 23 2s and 23 5s would make 23 10s or
\(2^{23}\cdot 5^{24}\cdot 7^3\) = \(10^{23}\cdot 5\cdot 7^3\)
\(10^{23}\) would give 23 0s.
Again, \(10^{23}\cdot 2,115 = 2,115\times10^{23}\)
So, the number \(2^{23}\cdot 5^{24}\cdot 7^3\) would have 4 + 23 = 27 digits.
Correct answer:
D
Hope this helps!
-Jay
_________________
Manhattan Review GMAT Prep
Locations:
GMAT Prep Indianapolis |
LSAT Prep Atlanta |
GRE San Antonio |
SAT Prep Detroit | and many more...
Schedule your free consultation with an experienced GMAT Prep Advisor!
Click here.
