Divisibility And Factors

To find the greatest value of

A%20%2B%20B

such that the 7-digit number 485A64B is divisible by both 8 and 9, we follow these steps:

Step 1: Divisibility by 8

A number is divisible by 8 if its last three digits are divisible by 8. Here, the last three digits are 64B. We need 64B to be divisible by 8. Let's test values of

B%3A%200%20%5Cleq%20B%20%5Cleq%209

Checking divisibility for each

B

B = 0: 640/8 = 80 (divisible)
B = 1: 641/8 = 80.125 (not divisible)
B = 2: 642/8 = 80.25 (not divisible)
B = 3: 643/8 = 80.375 (not divisible)
B = 4: 644/8 = 80.5 (not divisible)
B = 5: 645/8 = 80.625 (not divisible)
B = 6: 646/8 = 80.75 (not divisible)
B = 7: 647/8 = 80.875 (not divisible)
B = 8: 648/8 = 81 (divisible)
B = 9: 649/8 = 81.125 (not divisible)

The possible values of

B

that make 64B divisible by 8 are 0 and 8.

Step 2: Divisibility by 9

A number is divisible by 9 if the sum of its digits is divisible by 9. The sum of the digits in 485A64B is

4%20%2B%208%20%2B%205%20%2B%20A%20%2B%206%20%2B%204%20%2B%20B%20%3D%2027%20%2B%20A%20%2B%20B

Check divisibility for each

B

that works from Step 1:

B = 0: 27 + A + 0 must be divisible by 9.
B = 8: 27 + A + 8 = 35 + A must be divisible by 9.

For B = 0:

27%20%2B%20A

must be 36, 45, etc., so possible

A

= 9. Then,

A%20%2B%20B%20%3D%209%20%2B%200%20%3D%209.

For B = 8:

35%20%2B%20A

must be 36, 45, etc., so possible

A

= 1. Then,

A%20%2B%20B%20%3D%201%20%2B%208%20%3D%209.

Thus, the greatest value of

A%20%2B%20B

that satisfies both conditions is

9

The correct answer is

9

About Divisibility And Factors - CUET-UG

Divisibility And Factors is a vital chapter for CUET-UG aspirants. Mastering the concepts covered in this chapter is essential for securing a top rank.

By rigorously practicing the previous year questions associated with this chapter, you can identify high-yield topics, understand the examiner's perspective, and boost your confidence during the actual exam.

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Review the topic breakdown to see which sub-topics within Divisibility And Factors carry the most weight. Then, tackle the questions iteratively to solidify your understanding.

High-Yield Trend

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Official Solution

About Divisibility And Factors - CUET-UG

Frequently Asked Questions

Why focus on Divisibility And Factors PYQs?

How to best use this analysis?

Divisibility And Factors

High-Yield Trend

Chapter Questions 1 MCQs

Official Solution

About Divisibility And Factors - CUET-UG

Frequently Asked Questions

Why focus on Divisibility And Factors PYQs?

How to best use this analysis?

Chapter Questions
1 MCQs