# Basic Arithmetic

Which of the following number is perfectly divisible by 132?

[A]31218

[B]78520

[C]38148

[D]52020

**38148**

A number will divisible by 132 if that number is divisible by 3, 4, and 11. (132=3*4*11) First we look at option (a), because it is not divisible by 4 so it can not be correct. Now in option (b) since it is not divisible by 3, so it is also wrong, and again when we check option (c), in option (c) 38148 is perfectly divisible by 3, 4 and 11 also and option (d) is not divisible by 11, so option (c) is our answer.

What will be the correct value of x+y, if a number 653xy is perfectly divisible by 80?

[A]2

[B]3

[C]4

[D]6

**6**

Because we know that 80=8*10 or 80=16*5. Now y that is unit digit in number must be zero. Therefore 653xy=653×0, and 653×0 will be definitely divisible by 16 or we can say that 653x is must be divisible by 8. Thus last three digits numbers 53x must be divisible by 8, and at x=6, 53x is perfectly divisible by 8.

So x+y=6+0=0

If a number k35624 is divisible by 11, than what will be the value of k?

[A]2

[B]5

[C]7

[D]6

**6**

There are several methods to get the answer but here we will discuss best and shortest way. As per the divisibility rule of 11, the difference of sum of the digits at odd places and sum of the digits at even places must be 0, 11, 22, 33…. etc.

=> (4+6+3)-(2+5+k)=0/11/22…

=> (13)-(7+k)=0 [since 11/22… are not possible]

=> 13-7-k=0

=> k=6

So option (d) is right answer.

What will be the value of k if, a number 42573k is divisible by 72?

[A]4

[B]5

[C]6

[D]7

**6**

As per the rules of divisibility, if given number 42573k is divisible by 72 (divisor) then this number should be divisible by 9 and 8 both. So it is clear that option (b) and (d) can not be right answers, since unit digit can’t be odd number to be divisible by 8. Now option (a) and (c) can be tried out. Thus we can easily get the value of k=6. Hence option (c) is correct answer.

Numbers between 1 to 1000 which are divisible by 7?

[A]777

[B]142

[C]143

[D]None of these

**142**

Because to get numbers between 1 to 1000 which are divisible by 7 can be calculated very easily just only by dividing 1000 by 7, 1000/7=142.8571, so 142 numbers are there between 1 to 1000 are divisible by 7, thus option (b) is the right answer.

Including both the extreme values (55 and 555), How many numbers are there between from 55 to 555 are divisible by 5?

[A]100

[B]111

[C]101

[D]None of these

**101**

The sequence of this series is as follows 55, 60, 65, 70, 75, ……, 545, 550, 555. Now we can easily get the numbers between 55 to 555 which are divisible by 5 are (555-55/5)+1=101, here we added 1 from outside because in questin it said that both the extreme values are added in our particular series. So option (c) is right answer.

How many numbers are between 100 to 200?

[A]100

[B]101

[C]99

[D]None of these

**101**

This question is very easy, here we can get the numbers between 100 to 200 just by this simple calculation, (200-100) + 1 = 101. Here we have added 1 from outside because if in series 100 would be not added then we will do (200 – 100), but here in quesion 100 is added in our series so we have add 1.

In the set of {300, 301, 302, …., 498, 499, 500}, How many numbers will be divisible by 3?

[A]200

[B]66

[C]67

[D]None of these

**67**

The very first number in this series {300, 301, 302, …., 498, 499, 500} is 300 and last number is 498, so now we have to calculate the total numbers from 300 to 498, are divisible by 3 (498-300/3) + 1 = 67, here we added 1 because 498 and 300 both are divisible by 3. So the right answer is option (c).

How many numbers are there which are divisible by neither 5 nor 7, in the set {200, 201, 202, ….., 798, 799, 800}?

[A]411

[B]412

[C]410

[D]None of these

**411**

Because total numbers in the given set are : (800 – 200) + 1 = 601.

Since we have calculated number of numbers which are divisible by either 5 or 7 or both in just earlier question : (121 + 86) – 17 = 190.

So the number of numbers which are divisible by neither 5 nor 7 are : 601 – 190 = 411. Therefore option (a) is correct answer.

How many numbers are there which are divisible by neither 5 nor 7, in the set {200, 201, 202, ….., 798, 799, 800}?

[A]411

[B]412

[C]410

[D]None of these

**411**

Because total numbers in the given set are : (800 – 200) + 1 = 601.

Since we have calculated number of numbers which are divisible by either 5 or 7 or both in just earlier question : (121 + 86) – 17 = 190.

So the number of numbers which are divisible by neither 5 nor 7 are : 601 – 190 = 411. Therefore option (a) is correct answer.