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

Sail E0 Webinar

Question

If

R = \frac{(30^{65} - 29^{65})}{(30^{64} - 29^{64})}

, then (CAT 2005)

Options:

A . 0

B . 0.1

C . 0.5

D . R>1

Answer: Option D
:
D

R = \frac{30^{65} - 29^{65}}{30^{64} + 29^{64}}

∵ a^{n} - b^{n} = (a - b) (a^{n - 1} + a^{n - 2} b + a^{n - 3} b^{2} + . . . . . + b^{n - 1})

∴ R = \frac{(30 - 29) [30^{64} + (30^{63} \times 29) + . . . . + 29^{64}]}{30^{64} + 29^{64}}

∵ 30^{64} + 30^{63} \times 29 + . . . + 29^{64} > 30^{64} + 29^{64}

∴ R > 1

Hence, option 4.
Alternative approach: Unitary Method

R = \frac{(30^{65} - 29^{65})}{(30^{64} + 29^{64})}

If you take this number to be of the form 'n' and 'n+1' instead of 30 and 29, you can solve it using simple numbers like

1 (n)

and

2 (n + 1)

i.e

\frac{(2^{3} - 1^{3})}{(2^{2} + 1^{2})} = \frac{7}{5} > 1

. Only 1 option satisfies this. Option (d)

Was this answer helpful ?

Next Question

Submit Solution

More Questions on This Topic :

Question 1. Lety =12+13+12+13+....... What is the value of y?....

Question 2. Let a1=p and b1=q where p and q are positive quantities. Define an=pbn−1 and bn=qbn−1, for even n>1 and....the smallest odd n such that an+bn<0.01? (CAT 2007)

Question 3. Anita had to do a multiplication. Instead of taking 35 as one of the multipliers, she took 53. As a result, the product ....up by 540. What is the new product? (CAT 2001)

Question 4. Let n!=1×2×3×...........×n for integer n>1. If p=1!+(2+2!)+(3+3!)+...........+(10+10!), then p+2 ....when divided by 11! leaves a remainder of (CAT 2005)

Question 5. Three pieces of cakes of weights 412 lbs, 634 lbs and 715 lbs respectively are to be divided into parts of equal weights....maximum number of guests that could be entertained? (CAT 2001)

Question 6. Let x=√4+√4−x Then x equals : (CAT 2005)....

Question 7. The integers 1,2,...... 40 are written on a blackboard. The following operation is then repeated 39 times; in each repet....number left on the board at the end? (CAT 2007)

Question 8. What are the last two digits of 72008? (CAT 2008)....

Question 9. 992250 = 2a x 3b x 5c x 7d. The value of a+b+c+d is ....

Question 10. The number of employees in Obelix Menhir Co. is a prime number and is less than 300. The ratio of the number of employee....of employees who are not, can possibly be (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