**Arithmetic Tricks for SSC**

## প্রিয় পাঠক, বিভিন্ন ধরনের পাটিগণিত প্রশ্ন (Arithmetic Tricks for SSC) ) কিভাবে নির্ণয় করা যেতে পারে তার কিছু গুরুত্বপূর্ণ ট্রিকস এখানে দেওয়া হলো।

### পাটিগণিত – স্টাফ সিলেকশন কমিশন পরীক্ষার উপযোগী মিসলেনিয়াস প্রশ্ন- সেট 3

1)Find the sum of 18^{2} + 20^{2} + 22^{2} + …..+50^{2}

A)53582

B)73892

C)633552

D)21284

2)Find the unit’s digit of (496)^{496} x (524)^{524} x (1016)^{260}

A)4

B)2

C)6

D)8

3)Find the value of (1/2 + 1/4 + 1/12 + 1/20 + 1/30 + 1/42 + 1/56 + 1/72)

A)1/5840

B)15/36

C)1/18

D)35/36

4)The simplified form of 1038 (1/13) + 1038 (2/13) + 1038 (3/13) + 1038 (4/13) + 1038 (7/13) +1038 (9/13)

A)6130

B)6230

C)12456

D)6320

5)Find the sum of all multiplies of 15 from 12 to 120

A)540

B)450

C)625

D)490

6)How many even numbers are there between 1 and 499?

A)250

B)249

C)251

D)252

7)The product of two number is 4056 and their HCF is 26. The number of such pair is

A)1

B)2

C)3

D)4

8)The product of two numbers is 9 :10. Their HCF is 19 Their LCM is

A)1710

B)1900

C)3249

D)32490

9)4^{11} + 4^{12} + 4^{13} + 4^{14} is divisible by…………..

A)7

B)14

C)17

D)9

10)For what value of N,270N will be a perfect square, where 270N is a 4 digit number?

A)1

B)6

C)4

D)9

**Read More:** **Important QA Arithmetic Questions-How to do solve**

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**Arithmetic Questions for SSC : SOLUTION**

1.D)

The sum of the square of even numbers from 2 to n ={n(n+1) (n+2)}/6

2^{2} + 4^{2}+6^{2}+8^{2}+50^{2}= {50(50+1)(50+2)}/6=22100

And 2^{2}+4^{2}+ …+16^{2}= {16(16+1)(16+2)}/6=816

Now 18^{2} + 20^{2} + 22^{2} + …..50^{2}= 22100 -816= 21284

2.C)

If the last digit of a number is 6, that number raised to any power will give a number with its last digit as 6

Last digit of (496)^{496}=6

Similarly digit of (1016)^{260}=6

For a number with 4 as last digit, 4^{2n} with have 6 as the last digit

Last digit of (524)^{524}=6

Now 6 X6X6 will have its last digit as 6

Hence, required answer is 6

3.D)

(1/2 + 1/4 + 1/12 + 1/20 + 1/30 + 1/42 + 1/56 + 1/72)

=1/2 + 1/4+ (1/12 +1/20+ 1/42+ 1/56 +1/72)

=1/2 +1/4 + (1/3-1/9)

=35/36

4.B)

1038 (1/13) + 1038 (2/13) + 1038 (3/13) + 1038 (4/13) + 1038 (7/13) +1038

=6*1038 + (1/13 + 2/13 +3/13 + 4/13 + 7/13 + 9/13)

=6*1038 +26/13

6230

5.A)

Multiple of 15 number from 12 to 120 is 8 (15,30,45,60,75,90,105,120)

Now S_{n}= n/2 (First term + Last term) = 8/2(15 +120) =540

**Read More:-** **Unit Digit Math- How to do it in five seconds**

6.B)

Between 1st and 499th first even number is 2 and the last even number is 498

Common difference is 2

Then t_{n}=498 a=2 and common difference d= 2

Now t_{n}=a+ (n-1) d

498=2+(n-1)2

n=249

Hence the number of even numbers between 1 to 499 is 249

7.B)

HCF of two number is 26

Let the number be 26a & 26b

26a *26b= 4056

ab= (4056)/ (26*26) =6

(a, b) = (1,6) (2,3)

So required are (26 *1,26*6) and (26*2,26*3)

Number of such pairs is =2

8.A)

Ratio of numbers 9:10

HCF = 19

First number = (19*9)

Second number = (19*10)

LCM *HCF = product of two number

LCM * 19=171 * 190

LCM=1710

9.C)

4^{11} + 4^{12} + 4^{13} + 4^{14}

=4^{11} (1+4^{1}+4^{2}+4^{3})

=4^{11}(85)

So, 4^{11}(17 *5)

10.C)

Check the option

Put the value of N from option

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