The remainder on dividing given integers a and b by 7 are respectively 5 and 4. Then, the remainder when ab is divided by 7 is
(a). 5
(b). 4
(c). 0
(d). 6
Please share the steps to solve it as well..
Answers
Answer:
So, A mod 7 = 3, and B mod 7 = 5
use mod property,
(A + B ) mod 7 = (5 + 3) mod 7 = 1
(A-B) mod 7 = (3 - 5) mod 7 = (-2) mod 7 = (7–2) mod 7 = 5
-2 and 5 belong to same residue class.
The equivalence class of the integer a, is the set {… , a − 2n, a − n, a, a + n, a + 2n, …}. This set, consisting of the integers congruent to a modulo n, is called the congruence class or residue class or simply residue of the integer a, modulo n. When the modulus n is known from the context, that residue may also be denoted [a].
refer to link Modular arithmetic - Wikipedia for more.
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OTHER ANSWERS
Anand Venkatesan
Anand Venkatesan, Quant & Verbal Mentor at Eptitude
Answered Feb 5, 2018
The basic identity of a division is :
Dividend (number being divided) = Divisor x Quotient + Remainder
So, A = 7p + 3 and B = 7q + 5
Here p and q are the respective quotients (non-negative integer values).
Clearly, A - B = 7p + 3 - 7q - 5 = 7(p - q) - 2
Now on using the basic identity of a division, this equation implies that when (A - B) is divided by 7, the quotient is (p - q) and the remainder is -2.
However, the remainder (when dividing by 7) can only be integer values from 0 to 6. This means we need to make the remainder positive!
So we rewrite the above equation as: A - B = 7(p - q - 1 + 1) - 2
i.e. A - B = 7(p - q - 1) + 7 - 2
Hence, A - B = 7(p - q - 1) + 5
Again using the basic identity of a division, this means that when (A - B) is divided by 7, the quotient is (p - q - 1) and the remainder is 5.
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Kumar Abhishek
Kumar Abhishek
Answered Mar 16, 2018 · Author has 59 answers and 26.1k answer views
A=7x+3
B=7y+5
A-B=7(x-y)-2
A-B=7(x-y)-7+7–2 [by adding -7 and +7]
A-B=7(x-y-1)+5
As seen above, if we divide A-B by 7, the remainder will be 5.
2.3k Views · View 9 Upvoters
Sunilkumar Hp
Sunilkumar Hp, Sofware Engineer at Sakhatech Information Systems Private Limited (2017-present)
Answered Feb 5, 2018
lets consider a as 10 which will give reminder 3 and take 12 which will give reminder 12 then |10–12|=2 then 2/7 always gives reminder 2 only…, if
a/7=3 and b/7=5
a/7 - b/7 = 3–5
a-b = -2 hence its reminder we Take the smallest nonnegative number congruent to -2 modulo 7 i.e. 5.
1.4k Views
Jitendra Bana
Jitendra Bana
Answered Feb 13, 2018
A = 7x + 3
B = 7y + 5
Then
A-B = 7 ( x-y ) - 2
If A is greater than B
The remainder is 5 for A-B divided by 7 because the difference between A and B is 5 more than 7n
Where n = 1,2,3,4,5………
548 Views
Rik Sinha
Rik Sinha
Answered Feb 18, 2018
A is congruent to 3 mod 7
B is congruent to 5 mod 7
A-B is congruent to -2=5 mod7
Hence your answer is 5
299 Views
Ivan Tsatsarov
Ivan Tsatsarov, Database Expert at Xogito (2015-present)
Answered Feb 7, 2018
remainder=3–5=-2=5 (mod 7)
So answer is 5
Step-by-step explanation:
Step-by-step explanation:
ATQ
a/7=5
=>a=7*5=35
b/7=4
=>b=4*7=28
NOW
ab=35*28
ab/7=35*28/7=5*28=140