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10 Jun 2020, 03:40
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E
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
65%
(hard)
Question Stats:
61% (02:30) correct
39%
(02:21)
wrong
based on 126
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X = a.bc
If a, b and c denote the units, tenths and hundredths digits in the decimal representation of X above, what is the value of the product abc?
(1) 100X divided by 50 leaves a remainder 24
(2) 1000X divided by 8 leaves a remainder 0
Are You Up For the Challenge: 700 Level Questions
If a, b and c denote the units, tenths and hundredths digits in the decimal representation of X above, what is the value of the product abc?
(1) 100X divided by 50 leaves a remainder 24
(2) 1000X divided by 8 leaves a remainder 0
Are You Up For the Challenge: 700 Level Questions
yashikaaggarwal
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10 Jun 2020, 04:16
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IMO E
X = a.BC
Statement 1: 100X leaves 24 as remainder when divided by 50
The no. Leaving 24 as reminder when divided by 50 = 24,74,124,174,224..............
Therefore x value can be
100x = 24 => 0.24,
100x = 74 => 0.74
100x = 124 => 1.24
And so on.. (Insufficient)
Statement 2: 1000x don't leave remainder when divided by 8
The values not leaving remainder when divided by 8 = 8,16,24,32............1000,1008
Therefore x value can be
1000x = 08 => 0.008,
1000x = 16 => 0.016
1000x = 24 => 0.024.
1000x = 1000 => 1
1000x = 1008 => 1.008
And so on.. (Insufficient)
Statement 1&2 together.
No. In the set leaving remainder 24 when divided by 50 and not leaving remainder when divided by 8 = {24,124,224,324,424.......1240,2240.......}
Value of X can be = {1.24,2.24,3.24..........}
No particular answer
Posted from my mobile device
X = a.BC
Statement 1: 100X leaves 24 as remainder when divided by 50
The no. Leaving 24 as reminder when divided by 50 = 24,74,124,174,224..............
Therefore x value can be
100x = 24 => 0.24,
100x = 74 => 0.74
100x = 124 => 1.24
And so on.. (Insufficient)
Statement 2: 1000x don't leave remainder when divided by 8
The values not leaving remainder when divided by 8 = 8,16,24,32............1000,1008
Therefore x value can be
1000x = 08 => 0.008,
1000x = 16 => 0.016
1000x = 24 => 0.024.
1000x = 1000 => 1
1000x = 1008 => 1.008
And so on.. (Insufficient)
Statement 1&2 together.
No. In the set leaving remainder 24 when divided by 50 and not leaving remainder when divided by 8 = {24,124,224,324,424.......1240,2240.......}
Value of X can be = {1.24,2.24,3.24..........}
No particular answer
Posted from my mobile device
10 Jun 2020, 08:23
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Bunuel
100X is the number ABC, where A, B and C are digits. If this number gives us a remainder of 24 when we divide by 50, then its last two digits must either be 24 or 74. So the two digit number BC is either 24 or 74.
1000X is the number ABC0. If this number is divisible by 8, its last three digits, BC0, form a number divisible by 8.
Using both Statements together, we can conclude that BC must be 24, because 240 is divisible by 8 but 740 is not. But we have no information at all about the value of A, so no hope of finding a unique value for the product A*B*C, and the answer is E.
