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10 Apr 2017, 06:03
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A
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Difficulty:
95%
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Question Stats:
33% (03:26) correct
67%
(02:56)
wrong
based on 345
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In the number 1@3,52#, @ and # represent distinct digits. If 1@3,52# is a multiple of 18, is @ > #?
(1) 5@# is a multiple of 8
(2) 5@# is a multiple of 6
(1) 5@# is a multiple of 8
(2) 5@# is a multiple of 6
10 Apr 2017, 10:00
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notation: @ = a # = b
number 1a3,52b is divisible by 18, this means it is even and also divisible by 9. from here:
1. b is even
2. a+b + 1 + 3 + 5 + 2 is div by 9.
a+b is either 7 or 16.
if a+b = 7: a = 1 b = 6 or a = 3 b = 4 or a =5 b = 2 or a = 7 b = 0
if a + b = 16, a = 8 b = 8
statement 1:
5ab div by 8:
516 not div by 8.
534 not div by 8
552 is div by 8 - solution
570 not div by 8
Suff
statement 2:
5ab div by 6:
5 + a + b div by 3. if a + b = 7, then 5ab div by 3.
if a + b = 16, then a + b div by 3.
so can not narrow down a and b
Insuff
Answer: A
number 1a3,52b is divisible by 18, this means it is even and also divisible by 9. from here:
1. b is even
2. a+b + 1 + 3 + 5 + 2 is div by 9.
a+b is either 7 or 16.
if a+b = 7: a = 1 b = 6 or a = 3 b = 4 or a =5 b = 2 or a = 7 b = 0
if a + b = 16, a = 8 b = 8
statement 1:
5ab div by 8:
516 not div by 8.
534 not div by 8
552 is div by 8 - solution
570 not div by 8
Suff
statement 2:
5ab div by 6:
5 + a + b div by 3. if a + b = 7, then 5ab div by 3.
if a + b = 16, then a + b div by 3.
so can not narrow down a and b
Insuff
Answer: A
10 Apr 2017, 06:32
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godot53
Hi
1@352# div by 18 means
a) # is even
b) 1+@+3+5+2+# = 11+@+# should be div by 9..
c) (11+@+#)=9+(2+@+#)....
So @+# div by 9 should give us remainder 9-2 or 7, so when @+# is div by 3, remainder will be same as 7 div by 3 or it WILL be 1..
Let's see the statements..
(1) 5@# is a multiple of 8....
Most important point...
5+@+# will be div by 3 .....WHY?
11+@+# is div by 3..... So 6+5+@+# should be div by 3...
6 is div by 3, so remaining 5+@+# should also be div by 3
We are looking for a number 5@#, which is EVEN and multiple of 3
The first Number in 500s div by 8 is 504 and it is div by 3 also..
Next number in line will be 504+8*3=528, 528+24=552, 552+24=576,
In all these numbers 528,552,576 as possible values, ONLY 52 will leave a remainder of 7 when div by 9 (refer point (C) above)
Our ans is 552 and we can say 5>2 or @>#..
Sufficient
(2) 5@# is a multiple of 6.
Nothing new ..
We already know # is EVEN, so 5@# is even..
Also as explained in statement I, 5@# will be div by 3
So 5@# is div by 6 is already known.
Insufficient
A
