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03 Nov 2019, 00:24
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If ab is a 2-digit even number, is ab divisible by 4?
(1) \(\frac{a}{b}\) is a multiple of 4.
(2) \(a=b+1\)
(1) \(\frac{a}{b}\) is a multiple of 4.
(2) \(a=b+1\)
Chetan's questions
03 Nov 2019, 00:53
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If ab is a 2-digit even number, is ab divisible by 4?
ab can be written as '10*a + b' where 1≤a≤9 and b = 0,2,4,6 or 8(any one)
Hence 10 ≤ ab ≤ 98 (only even numbers)
(I) ab is a multiple of 4.
ab = 4k where k is an integer i.e. k = 1 ,2 , 3, 4....
ab = 4, 8, 12, 16, 20 ... so on... till 96
OR
\(\frac{ab}{4}\) = 3, 4, 5 .. . .. 24
So irrespective of individual values of a and b ab is divisible of 4.
SUFFICIENT.
(II) a=b+1
a > b
Possible values of ab are with divisibility as follows:
b = 0 a = 1 ab = 10 NO
b = 2 a = 3 ab = 32 YES
b = 4 a = 5 ab = 54 NO
b = 6 a = 7 ab = 76 YES
b = 8 a = 9 ab = 98 NO
INSUFFICIENT.
IMO Answer A.
ab can be written as '10*a + b' where 1≤a≤9 and b = 0,2,4,6 or 8(any one)
Hence 10 ≤ ab ≤ 98 (only even numbers)
(I) ab is a multiple of 4.
ab = 4k where k is an integer i.e. k = 1 ,2 , 3, 4....
ab = 4, 8, 12, 16, 20 ... so on... till 96
OR
\(\frac{ab}{4}\) = 3, 4, 5 .. . .. 24
So irrespective of individual values of a and b ab is divisible of 4.
SUFFICIENT.
(II) a=b+1
a > b
Possible values of ab are with divisibility as follows:
b = 0 a = 1 ab = 10 NO
b = 2 a = 3 ab = 32 YES
b = 4 a = 5 ab = 54 NO
b = 6 a = 7 ab = 76 YES
b = 8 a = 9 ab = 98 NO
INSUFFICIENT.
IMO Answer A.
03 Nov 2019, 01:34
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You took first statement wrong.
It is a/b, not ab, in first statement.
Moreover, b can take 0, 2, 4, 6, 8 only.
Statement- 1
a/b is multiple of 4.
So I can write it as
a= 4bk. k is natural no. such as 1, 2, 3....
For b = 2, k =1
a=8, then ab = 82, not divisible by 4.
but For b= 0, and any value of k
a= 0, ab=00
divisible by 4. But 00 is not considered 2 digit even no.
For b = 4, k =1
a=16, But a is single digit so this option is not considerable.
So at all , sufficient.
For statement- 2
a= b+1, 10,32,54,76,98
take ab= 10, not divisible
take 32, divisible by 4.
Not sufficient
For st-1+2
Combining both statement is also not sufficient.
A is answer.
It is a/b, not ab, in first statement.
Moreover, b can take 0, 2, 4, 6, 8 only.
Statement- 1
a/b is multiple of 4.
So I can write it as
a= 4bk. k is natural no. such as 1, 2, 3....
For b = 2, k =1
a=8, then ab = 82, not divisible by 4.
but For b= 0, and any value of k
a= 0, ab=00
divisible by 4. But 00 is not considered 2 digit even no.
For b = 4, k =1
a=16, But a is single digit so this option is not considerable.
So at all , sufficient.
For statement- 2
a= b+1, 10,32,54,76,98
take ab= 10, not divisible
take 32, divisible by 4.
Not sufficient
For st-1+2
Combining both statement is also not sufficient.
A is answer.
lnm87
If ab is a 2-digit even number, is ab divisible by 4?
ab can be written as '10*a + b' where 1≤a≤9 and b = 0,2,4,6 or 8(any one)
Hence 10 ≤ ab ≤ 98 (only even numbers)
(I) ab is a multiple of 4.
ab = 4k where k is an integer i.e. k = 1 ,2 , 3, 4....
ab = 4, 8, 12, 16, 20 ... so on... till 96
OR
\(\frac{ab}{4}\) = 3, 4, 5 .. . .. 24
So irrespective of individual values of a and b ab is divisible of 4.
SUFFICIENT.
(II) a=b+1
a > b
Possible values of ab are with divisibility as follows:
b = 0 a = 1 ab = 10 NO
b = 2 a = 3 ab = 32 YES
b = 4 a = 5 ab = 54 NO
b = 6 a = 7 ab = 76 YES
b = 8 a = 9 ab = 98 NO
INSUFFICIENT.
IMO Answer A.
ab can be written as '10*a + b' where 1≤a≤9 and b = 0,2,4,6 or 8(any one)
Hence 10 ≤ ab ≤ 98 (only even numbers)
(I) ab is a multiple of 4.
ab = 4k where k is an integer i.e. k = 1 ,2 , 3, 4....
ab = 4, 8, 12, 16, 20 ... so on... till 96
OR
\(\frac{ab}{4}\) = 3, 4, 5 .. . .. 24
So irrespective of individual values of a and b ab is divisible of 4.
SUFFICIENT.
(II) a=b+1
a > b
Possible values of ab are with divisibility as follows:
b = 0 a = 1 ab = 10 NO
b = 2 a = 3 ab = 32 YES
b = 4 a = 5 ab = 54 NO
b = 6 a = 7 ab = 76 YES
b = 8 a = 9 ab = 98 NO
INSUFFICIENT.
IMO Answer A.
