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![What is the 6th digit from the left of [m]202^3[/m]?](/forum/styles/gmatclub_light/imageset/icon_post_target_unread.svg "What is the 6th digit from the left of [m]202^3[/m]?"){kind=icon}
22 Aug 2024, 01:30
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A
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
45%
(medium)
Question Stats:
65% (01:24) correct
35%
(01:21)
wrong
based on 284
sessions
History
Date
Time
Result
Not Attempted Yet
What is the 6th digit from the left of \(202^3\)?
A. 0
B. 2
C. 4
D. 6
E. 8
A. 0
B. 2
C. 4
D. 6
E. 8
22 Aug 2024, 05:13
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\(202^3\) can be written as \(101^3 * 2^3\)
=> \(101^2\) * 101 * 8
=> \((100 + 1)^2\) * 101 * 8
=> (10000 + 200 + 1) * 101 * 8
=> (10201) * (100 + 1) * 8
=> (1020100 + 10201) * 8
=> (1030301) * 8
=> 8242408
6th digit is 0
Answer A.
=> \(101^2\) * 101 * 8
=> \((100 + 1)^2\) * 101 * 8
=> (10000 + 200 + 1) * 101 * 8
=> (10201) * (100 + 1) * 8
=> (1020100 + 10201) * 8
=> (1030301) * 8
=> 8242408
6th digit is 0
Answer A.
General Discussion
22 Aug 2024, 02:15
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To gain insight, treat \(202^3\) as \(200^3\). \(200^3 = 8 000 000\) has 7 digits and therefore the 6th digit from the left will be the tens digit. \(202^3\) will also yield a 7 digit number.
Looking at this as if it were being done through long multiplication:
ie:
\( 202\)
\(* 202\)
\(* 202\)
\(---\)
Focusing on the units digit in \(202^3\): \(2^3 = 8\), so nothing is carried over to the tens digit.
The tens digit will be made from the sum of the multiplication of each of the units digits with each of the tens digits. The tens digit in \(202^3\) is \(0\) which means that every multiplication done with each of the units digits will yield \(0\).
As nothing is carried over from the multiplication of the unitis digits with each other, the tens digit of \(202^3\) will be \(0\)
ANSWER A
Looking at this as if it were being done through long multiplication:
ie:
\( 202\)
\(* 202\)
\(* 202\)
\(---\)
Focusing on the units digit in \(202^3\): \(2^3 = 8\), so nothing is carried over to the tens digit.
The tens digit will be made from the sum of the multiplication of each of the units digits with each of the tens digits. The tens digit in \(202^3\) is \(0\) which means that every multiplication done with each of the units digits will yield \(0\).
As nothing is carried over from the multiplication of the unitis digits with each other, the tens digit of \(202^3\) will be \(0\)
ANSWER A
