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09 Feb 2012, 23:39
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43% (02:59) correct
57%
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based on 639
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Shaina's five-distinct-digit locker code is 5A48B. What digit letter A symbolizes in Shaina's locker code?
(1) Shaina's locker code is divisible by all integers 2 through 6.
(2) Shaina's locker code is divisible by 9 and 11.
(1) Shaina's locker code is divisible by all integers 2 through 6.
(2) Shaina's locker code is divisible by 9 and 11.
10 Feb 2012, 00:47
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Shaina's five-distinct-digit locker code is 5A48B. What digit letter A symbolizes in Shaina's locker code?
(1) Shaina's locker code is divisible by all integers 2 through 6.
Since the number is divisible by 5 and 2 the B must be 0 (notice that in this case it will also be divisible by 4: a number is divisible by 4 if the last two digits form a number divisible by 4, since 80 is divisible by for so is the number);
The number is also divisible by 3, which means that the sum of the digits must be a multiple of 3: 5+A+4+8+0=17+A ---> A must be 1, or 7. Thus we have two different values of the number. Not sufficient.
(2) Shaina's locker code is divisible by 9 and 11
Divisibility by 9 and 11:
If the sum of the digits is divisible by 9, so is the number --> 5+A+4+8+B=17+A+B=multiple of 9 --> A+B is 1 or 10;
If you sum every second digit and then subtract all other digits and the answer is divisible by 11, then the number is divisible by 11 --> (5+4+B)-(A+8)=1+B-A=multiple of 11 --> B-A=-1 or B-A=10 (not possible, as A and B must be digits and their difference can not be 10);
If A+B=1 and B-A=-1 --> A=1 and B=0;
If A+B=10 and B-A=-1 --> A=5.5 and B=4.5 (not possible as A and B must be digits);
We have only one value of the number: 51480. Sufficient.
Answer: B.
(1) Shaina's locker code is divisible by all integers 2 through 6.
Since the number is divisible by 5 and 2 the B must be 0 (notice that in this case it will also be divisible by 4: a number is divisible by 4 if the last two digits form a number divisible by 4, since 80 is divisible by for so is the number);
The number is also divisible by 3, which means that the sum of the digits must be a multiple of 3: 5+A+4+8+0=17+A ---> A must be 1, or 7. Thus we have two different values of the number. Not sufficient.
(2) Shaina's locker code is divisible by 9 and 11
Divisibility by 9 and 11:
If the sum of the digits is divisible by 9, so is the number --> 5+A+4+8+B=17+A+B=multiple of 9 --> A+B is 1 or 10;
If you sum every second digit and then subtract all other digits and the answer is divisible by 11, then the number is divisible by 11 --> (5+4+B)-(A+8)=1+B-A=multiple of 11 --> B-A=-1 or B-A=10 (not possible, as A and B must be digits and their difference can not be 10);
If A+B=1 and B-A=-1 --> A=1 and B=0;
If A+B=10 and B-A=-1 --> A=5.5 and B=4.5 (not possible as A and B must be digits);
We have only one value of the number: 51480. Sufficient.
Answer: B.
10 Feb 2012, 00:27
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Smita04
Shaina's five-distinct-digit locker code is 5A48B. What digit letter A symbolizes in Shaina's locker code?
(1) Shaina's locker code is divisible by all integers 2 through 6.
(2) Shaina's locker code is divisible by 9 and 11.
(1) Shaina's locker code is divisible by all integers 2 through 6.
(2) Shaina's locker code is divisible by 9 and 11.
nice question
(1) says 5A48B is divisible by 2, 3, 4, 5, 6..IF that be so we need to find what does B represents here...since B is divisible by 5 , the value of B can either be 0 or 5...if the value of B is 5, then 5A48B is not divisible by 2,4 and 6 (5A485 is not divisible by 2,4 and 6) thus the value of B is 0 here
so the new term is 5A480..in order for 5A480 to be divisible by 3 or 6( 2 x 3), the total sum of digits should be divisible by 3 so the total makes it 17 + A, now A could be either 1 (total =18) or 4 (total = 21) or 7( total = 24) , thus (1) is not sufficient enough to answer.
lets move to (2) now,
5A48B is divisible by 9 and 11..taking them one by one, to be divisible by 9 , the total should be divisible by 9, the total is 17 + A+B, so A+ B could be either 1( total 18) or 10 ( total 27)
now if the total of A + B is 1, then either A is 0 and B is 1 or A is 1 and B is 0
as we plug them in
the number would be either 50481 or 51480
only 51480 is divisible by 11
so (2) correctly gives the value of A
IMO B
correct me if i am wrong.
