Shortcuts 3

# Shortcuts 3 - To find out if a number is divisible by...

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To find out if a number is divisible by seven: Take the last digit, double it, and subtract it from the rest of the number. If the answer is more than a 2 digit number perform the above again. If the result is 0 or is divisible by 7 the original number is also divisible by 7. Example 1 ) 259 9*2= 18. 25-18 = 7 which is divisible by 7 so 259 is also divisible by 7. Example 2 ) 2793 3*2= 6 279-6= 273 now 3*2=6 27-6= 21 which is divisible by 7 so 2793 is also divisible by 7 . Now find out if following are divisible by 7 1) 2841 2) 3873 3) 1393 4) 2877 TO FIND SQUARE OF A NUMBER BETWEEN 40 to 50 Sq (44) . 1) Subtract the number from 50 getting result A. 2) Square A getting result X. 3) Subtract A from 25 getting result Y 4) Answer is xy EXAMPLE 1 : 44 50-44=6 Sq of 6 =36 25-6 = 19 So answer 1936 EXAMPLE 2 : 47 50-47=3 Sq 0f 3 = 09 25-3= 22 So answer = 2209 NOW TRY To Find Sq of 48 ,26 and 49 TO FIND SQUARE OF A 3 DIGIT NUMBER : LET THE NUMBER BE XYZ

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SQ (XYZ) is calculated like this STEP 1. Last digit = last digit of SQ(Z) STEP 2. Second Last Digit = 2*Y*Z + any carryover from STEP 1. STEP 3. Third Last Digit 2*X*Z+ Sq(Y) + any carryover from STEP 2. STEP 4. Fourth last digit is 2*X*Y + any carryover from STEP 3. STEP 5 . In the beginning of result will be Sq(X) + any carryover from Step 4. EXAMPLE : SQ (431) STEP 1. Last digit = last digit of SQ(1) =1 STEP 2. Second Last Digit = 2*3*1 + any carryover from STEP 1.= 6 STEP 3. Third Last Digit 2*4*1+ Sq(3) + any carryover from STEP 2.= 2*4*1 +9= 17. so 7 and 1 carryover STEP 4. Fourth last digit is 2*4*3 + any carryover (which is 1) . = 24+1=25. So 5 and carry over 2. STEP 5 . In the beginning of result will be Sq(4) + any carryover from Step 4. So 16+2 =18. So the result will be 185761. If the option provided to you are such that the last two digits are different, then you need to carry out first two steps only , thus saving time. You may save up to 30 seconds on each calculations and if there are 4 such questions you save 2 minutes which may really affect UR Percentile score. PYTHAGORAS THEROEM :
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## This note was uploaded on 01/27/2010 for the course EE 100 taught by Professor Abc during the Spring '10 term at Punjab Engineering College.

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Shortcuts 3 - To find out if a number is divisible by...

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