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86% (01:44) correct
14%
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x is a positive integer less than 100. When x is divided by 5, the remainder is 4, and when x is divided by 23, the remainder is 7. What is the value of x?
A. 7
B. 30
C. 53
D. 76
E. 99
_________________
A. 7
B. 30
C. 53
D. 76
E. 99
_________________
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Archit3110
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Bunuel
Clearly option E..
99= 5*19+4 and 99=23*4+7
Bunuel
x=5q+4
x=23p+7
→23p-5q=-3
if 5q has a 5 units digit,
then 23p must have a 2 units digit
try 4*23=92
92-5*19=-3 yes
p=4, q=19,
and n=99
E
Posts: 2
X=5a+4
X=23b+7
5a has to be divisible by 5 and total has to be less than 100, so a must have to be less than 20. Take a=19, that will give u value of X=99.
Now check second equation. Divide 99 by 23 and u will find a remainder of 7. As (23*4=92). So 99 works.
So ans is 99.
X=23b+7
5a has to be divisible by 5 and total has to be less than 100, so a must have to be less than 20. Take a=19, that will give u value of X=99.
Now check second equation. Divide 99 by 23 and u will find a remainder of 7. As (23*4=92). So 99 works.
So ans is 99.
Bunuel
Take multiples of 23 & keep adding 7 to the number (<100). For every such number check if it's ending with 4 or 9.
Only option when divided by 5 gives remainder 4 is 99, hence it is the answer choice
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TheNightKing
Joined: 18 Dec 2017
Last visit: 20 Mar 2024
Posts: 1,119
Location: United States (KS)
GMAT 1: 600 Q46 V27
GMAT 1: 600 Q46 V27
Posts: 1,119
Bunuel
Use options.
Only option E, which is 99, gives us remainder 4 when divided by 5. NO need to check anything else.
Answer E
When x is divided by 5, the remainder is 4
Dividend = Divisor * Quotient + Remainder
=> x = 5*k + 4 (where k is an integer)
=> x = 5k + 4
when x is divided by 23, the remainder is 7
=> x = 23t + 7 (where t is an integer)
=> x = 5k + 4 = 23t + 7
=> 5k = 23t + 3
=> k = \(\frac{23t + 3}{5}\)
Only those values of t which will give k also as an integer are the possible values
=> t = 4 and k = \(\frac{23*4 + 3}{5}\) = 19
=> n = 5k + 4 = 5*19 + 4 = 99
So, Answer will be E
Hope it helps!
Watch the following video to MASTER Remainders
_________________
Dividend = Divisor * Quotient + Remainder
=> x = 5*k + 4 (where k is an integer)
=> x = 5k + 4
when x is divided by 23, the remainder is 7
=> x = 23t + 7 (where t is an integer)
=> x = 5k + 4 = 23t + 7
=> 5k = 23t + 3
=> k = \(\frac{23t + 3}{5}\)
Only those values of t which will give k also as an integer are the possible values
=> t = 4 and k = \(\frac{23*4 + 3}{5}\) = 19
=> n = 5k + 4 = 5*19 + 4 = 99
So, Answer will be E
Hope it helps!
Watch the following video to MASTER Remainders
_________________
How to Solve :
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
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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