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When a positive integer x is divided by 91, the remainder is 49. What is the remainder when 2x is divided by 13 ?
A. 0
B. 7
C. 10
D. 12
E. 49
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A. 0
B. 7
C. 10
D. 12
E. 49
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---ASIDE---------------
If N divided by D leaves remainder R, then the possible values of N are R, R+D, R+2D, R+3D,. . . etc.
For example, if k divided by 5 leaves a remainder of 1, then the possible values of k are: 1, 1+5, 1+(2)(5), 1+(3)(5), 1+(4)(5), . . . etc.
-----------------------
When a positive integer x is divided by 91, the remainder is 49
So, the smallest possible value of x is 49
What is the remainder when 2x is divided by 13 ?
Plug in our x-value to get: What is the remainder when 2(49) is divided by 13 ?
Simplify to get: What is the remainder when 98 is divided by 13 ?
98 divided by 13 equals 7 with remainder 7
Answer: B
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We can express x in the form of pq + r, in which p is the divisor , q is the quotient and r is the remainder.
x = 91q + 49
2x = (91*2)q + 98
2x = (91*2)q + 91 + 7
The remainder when 2x is divided by is the sum of individual remainder.
Option B
_________________
x = 91q + 49
2x = (91*2)q + 98
2x = (91*2)q + 91 + 7
The remainder when 2x is divided by is the sum of individual remainder.
Option B
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Power of Tiny Gains
1.01^(365) = 37.78
0.99^(365) = 0.03
Power of Tiny Gains
1.01^(365) = 37.78
0.99^(365) = 0.03
↧↧↧ Detailed Video Solution to the Problem ↧↧↧
When a positive integer x is divided by 91, the remainder is 49
Dividend = Divisor * Quotient + Remainders
Dividend = x
Divisor = 91
Quotient = k (assume)
Remainder = 49
=> x = 91*k + 49 = 91k + 49
What is the remainder when 2x is divided by 13
2x = 2 * (91k + 49) = 2*7*13k + 98
Remainder of 2x by 13 = Remainder of (2*7*13k + 98) by 13
= Remainder of 2*7*13k by 13 + Remainder of 98 by 13
= 0 + 7 = 7
So, Answer will be B
Hope it helps!
Playlist on Solved Problems on Remainders here
Watch the following video to MASTER Remainders
_________________
When a positive integer x is divided by 91, the remainder is 49
Dividend = Divisor * Quotient + Remainders
Dividend = x
Divisor = 91
Quotient = k (assume)
Remainder = 49
=> x = 91*k + 49 = 91k + 49
What is the remainder when 2x is divided by 13
2x = 2 * (91k + 49) = 2*7*13k + 98
Remainder of 2x by 13 = Remainder of (2*7*13k + 98) by 13
= Remainder of 2*7*13k by 13 + Remainder of 98 by 13
= 0 + 7 = 7
So, Answer will be B
Hope it helps!
Playlist on Solved Problems on Remainders here
Watch the following video to MASTER Remainders
_________________
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GMAT Club Topic Wise Problems
All Quant Topics Theory || Last Two Digits of Exponents Ending with 1, 2, 3, 4, 5, 6, 7, 8, 9 || Units' Digit Problems || Even and Odd || Divisibility Rules || Positive and Negative || Absolute Value Basics || Inequalities || Absolute Value + Inequality || Functions and Custom Characters || LCM & GCD || Remainders || Factors and Multiples || Arithmetic and Geometric Progression || Co-ordinate Geometry || Circles || Probability: Coin Toss || Work Rate || Statistics || Stem & Leaf Plot || Box And Whisker Plot
GMAT Club Topic Wise Problems
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