Question 138

Find the greatest number which on dividing 70 and 50 leaves remainders 1 and 4 respectively

Solution

Share

Let the number be A.
As 70 leaves 1 remainder when divided by A, it could be written as: 70 = Ax + 1 where x is the quotient.
Similarly, 50 = Ay + 4.
Subtracting the equations, we get: 20 = A(x - y) - 3 ==> A(x-y) = 23.
23 can be expressed as a product of 2 numbers in only 1 way as 23 is a prime number.
So, A can either be 23 or 1 and the greatest value that A can take is 23.

Get AI Help

View More Questions From Number Systems

Create a FREE account and get:

  • Download Maths Shortcuts PDF
  • Get 300+ previous papers with solutions PDF
  • 500+ Online Tests for Free

CAT Quant Questions | CAT Quantitative Ability

CAT Simple Interest Compound Interest QuestionsCAT Averages QuestionsCAT Time, Speed and Distance QuestionsCAT Progressions and Series QuestionsCAT Time Speed Distance Questions

CAT DILR Questions | LRDI Questions For CAT

CAT DI with connected data sets QuestionsCAT Miscellaneous LR QuestionsCAT Quant Based LR QuestionsCAT Charts QuestionsCAT Selection With Condition Questions

CAT Verbal Ability Questions | VARC Questions For CAT

CAT Reading Comprehension QuestionsCAT Vocabulary QuestionsCAT Critical Reasoning QuestionsCAT Odd One Out QuestionsCAT Para Summary Questions

Free CAT Quant Questions

CAT InequalitiesCAT Quadratic EquationsCAT Data SufficiencyCAT Number SeriesCAT MiscellaneousCAT Simple Interest Compound InterestCAT AveragesCAT Time Speed DistanceCAT Coordinate GeometryCAT Logarithms, Surds and IndicesCAT Time And WorkCAT LogarithmsCAT Number SystemsCAT Time, Speed and DistanceCAT Linear EquationsCAT Probability, CombinatoricsCAT RemaindersCAT ArithmeticCAT Progressions and SeriesCAT AlgebraCAT Venn DiagramsCAT Averages Mixtures AlligationsCAT Profit And LossCAT Profit and LossCAT GeometryCAT MensurationCAT Functions, Graphs and StatisticsCAT PercentagesCAT Averages, Ratio and Proportion

Book Free CAT Mentorship

Get personalized CAT strategy from a 99%iler

500+ students mentored
CAT mentor

Join CAT 2026 course by 5-Time CAT 100%iler

Start your IIM journey with the right preparation and crack CAT 2026.

Enroll Now
Ask AI