L Let D be a recurring decimal of the form D=0. a1a2a1a2a1a2............;

Sail E0 Webinar

Question

L Let D be a recurring decimal of the form $D = 0. a_{1} a_{2} a_{1} a_{2} a_{1} a_{2} . . . . . . . . . . . .;$ where digits $a_{1}$ and $a_{2}$ lie between 0 and 9. Further, at most one of them is zero. Which of the following numbers necessarily produces an integer, when multiplied by D? (CAT 2000)

Options:

A . 18

B . 108

C . 198

D . 288

Answer: Option C
:
C

Ans: (c)

$D = 0. a_{1} a_{2}; 100 D = a_{1} a_{2} . a_{1} a_{2}$ (recurring); Thus, $99 D = a_{1} a_{2}; \Rightarrow D = (\frac{a_{1} a_{2}}{99})$

Required number should thus be a multiple of 99. Hence 198 is the required number.

Was this answer helpful ?

Next Question

Submit Solution

More Questions on This Topic :

Question 1. Three pieces of cakes of weights 412 lbs, 634 lbs and 715 lbs respectively are to be divided into parts of equal weigh....maximum number of guests that could be entertained? (CAT 2001)

Question 2. Anita had to do a multiplication. Instead of taking 35 as one of the multipliers, she took 53. As a result, the produc....up by 540. What is the new product? (CAT 2001)

Question 3. Lety =12+13+12+13+....... What is the value of y? ....

Question 4. Let S be a set of positive integers such that every element n of S satisfies the conditions I. 1000≤n"....many elements of S are divisible by 3? (CAT 2005)

Question 5. Let x=√4+√4−x Then x equals : (CAT 2005) ....

Question 6. Let n!=1×2×3×...........×n for integer n>1. If p=1!+(2+2!)+(3+3!)+...........+(10+10!), then p+....when divided by 11! leaves a remainder of (CAT 2005)

Question 7. If R=(3065−2965)(3064−2964) , then (CAT 2005) ....

Question 8. If x=(163+173+183+193), then x divided by 70 leaves a reminder of? (CAT 2005) ....

Question 9. When you reverse the digits of the number 13, the number increases by 18. How many other two digit numbers increase by....increase by 18 when their digits are reversed? (CAT 2006)

Question 10. The sum of four consecutive two digit odd numbers, when divided by 10, becomes a perfect square. Which of the followin....can possibly be one of these four members? (CAT 2006)

Chapter 1 - GLOBAL STEEL SCENARIO & INDIAN STEEL INDUSTRY Part 1 : (13-04-2024) INDUSTRY AND COMPANY AWARENESS (ICA)

Direction Sense Test Part 1 Reasoning (Hindi)

Chapter 1 - RMHP / OHP / OB & BP Part 1 : (14-02-2024) GPOE

Cube & Cuboid Part 1 Reasoning (Hindi)

Data Interpretation (DI) Basic Concept Reasoning (Hindi)

Counting Figures Part 1 Counting Of Straight Lines Reasoning (Hindi)

Sail E0 free webinar Webinars

Real Numbers Part 7 Class 10 Maths

Real Numbers Part 1 Class 10 Maths

Polynomials Part 1 Class 10 Maths

DSP Combined 1 Free Revision Test SAIL JO E-0

GPOE / GPA Combined 1 Free Revision Test SAIL JO E-0

BSP Plant Specific Review Test SAIL JO E-0

BSL Combined 1 Free Revision Test SAIL JO E-0

GFM Combined 1 Free Revision Test SAIL JO E-0