Know Yourself

Answers of Day 58:     1. 1/90.     2. 20 Problems to solve: 1. The product of two numbers is 33 and the sum of their squares is 130. Find their difference. 2. The sum of two numbers is 100 and their difference is 20. Find their product.

Subtle Thesaurus: Adjective : fine, skilful                    slight, nice, thin, delicate, understand, quiet, ingenious, clever, shrewd...  Antonyms : unsubtle, harsh ...  Example sentences:         ·         It was too difficult to identify the  subtle changes.   ·        There are only subtle differences between the brothers.        

Answers of Day 57 :     1. 10     2. 11 Problems to solve: 1. The difference between 2 numbers is 1 and their product is 90. Find the difference of their reciprocals. 2. The product of two numbers is 100 and the quotient, when the larger one is divided by the smaller one is 4. Find the larger number.

Snoopy Thesaurus: Adjective : curious                   interested, nosy, peering, questioning, investigate, inspecting, examining...  Antonyms : ignorant ...  Example sentences:         ·         She is such a snoopy lady.  ·        He called his snoopy friends to solve his dilemma.        

Problems to solve: 1.  The difference between the squares of two numbers is 160. The difference between the two numbers is 16. Find their sum. 2. The sum of the 4 consecutive odd numbers is 32. Find the largest number among them. 

Veer Thesaurus: Verb : change direction            bend, curve, cut, depart, deflect, twist, divert, drift, shift, turn...  Antonyms : stay, maintain ...  Example sentences:         ·         Veer right after the temple.   ·        He'll veer away from that situation anyway.        

Yearn Thesaurus: Verb : desire strongly            crave, long, want, wish for...  Antonyms : dislike, hate ...  Example sentences:         ·         That kid yearns for that chocolate.  ·        He yearned to live long.        

Problems on Numbers: 1. The product of 3 even consecutive numbers when divided by 5 is 335. The product of their square roots is: Solution:                Let the numbers be x, x+2 and x+4.                x(x+2)(x+4) / 5 = 335                x(x+2)(x+4) = 1675                [ x(x+2)(x+4) ] 1/2  = 5(67) 1/2   2. The sum of the three consecutive multiples of 5 is 375. What's the middle number? Solution:                 Let the 3 numbers be 5x, 5(x+1), 5(x+2).                 5x+5(x+1)+5(x+2) = 375                 5x+5x+5+5x+10 = 375                 15x+15 = 375                  15x = 360                      x= 24.                 The middle number is 5(x+1) = 5(25) = 125.

Dilemma Thesaurus: Noun : problem            double bind, difficulty, crisis, embarrassment, mess, puzzle...  Antonyms :  solution...  Example sentences:                  That's a serious dilemma we should think about that.          He'll never share his dilemma with anyone. 

Problems On Numbers 1. The difference between the squares of two numbers is 28000 and the sum of their numbers is 400. Find the numbers. Solution:                 Let the 2 numbers be x and y.                 (x 2 -y 2 ) / (x+y) = 28000/400                 (x+y)(x-y) / (x+y) =  70                 x-y = 70 ------ Equation 1                 x+y = 400 ---- Equation 2                 By solving equations 1 and 2 we get,                 x = 235 and y = 165.                 The numbers are 235 and 165. 2. The sum of three consecutive numbers is 315. The middle number is: Solution:                 Let the numbers be x, x+1 and x+2.                 x+x+1+x+2 = 315                 3x+3 = 315                     3x =  312                       x = 104.                 The middle number is x+1 = 105.                                         

Prudent Thesaurus: Adjective : wise                    tactical, careful, thinking twice, educated, sane, insightful, clever, aware...  Antonyms :  careless, imprudent, unwise..  Example sentences:         ·          He is such a prudent student. ·        It's prudent to call the doctor promptly.        

Problems on Numbers: 1. Two numbers such that the square of one is 171 less than seven times the square of the other. If the numbers are in the ratio of 2:3, the numbers are: Solution:                  Let the numbers be 2x and 3x.                  7(2x 2 )-(3x) 2 = 171                  28x 2 -9x 2 = 171                  19x 2 = 171                      x 2 =9                      x=3.                  The numbers are 6 and 9. 2. The difference of 2 positive integers multiplied by the bigger number is 85 and their sum multiplied by the smaller number is 99. Find the sum of their squares. Solution:                 Let the bigger number be x and the smaller number be y.                 (x-y)x = 85    [Condition 1]                  x 2 -xy = 85   ------- Equation 1                 (x+y)y = 99   [Condition 2]                  xy+ y 2 =99    ------- Equation 2                 By adding equation 1 and 2, we get                    x 2 +y 2 =

Obsolete Thesaurus: Adjective : no longer in use or practice                   out-of-date, old-fashioned, gone, discarded, antique...  Antonyms :  modern,new, up-to-date, current...  Example sentences:         ·          Female infanticide is obsolete. ·        These old equipments are obsolete.       

Problems on numbers 1. The sum of the 2 numbers is 15 and their product is 26. What will be the sum of their reciprocals? Solution:                Let the 2 numbers be x and y.                (1/x)+(1/y)= y+x/xy                                 = 15/26. 2.  If the sum of 2 numbers 35 and the sum of their squares is 625. Find their product. Solution:                 Let the numbers be x and y.                 x+y = 35                 x 2 +y 2 = 625                 2xy = x 2 +y 2 +2xy-(x 2 +y 2 )                        = (x+y) 2 - (x 2 +y 2 )                        = 35 2 -625                        = 1225-625                 2xy = 600                  xy  = 300.

Problems on Numbers 1. The product of two numbers is 27 and the quotient, when the larger one is divided by the smaller, is 3. What's the sum of the 2 numbers? Solution:                 Let the two numbers be x and y.                 xy = 27 ------ Equation 1                 x/y = 3                 x=3y                 Substitude x value in equation 1, we get                 3y 2  = 27                   y = 3.                 Hence,  x=9.                 Their sum is 9+3 = 12. 2. The difference between 2 numbers is 20. When the larger number is divided by the smaller one, the quotient is 2 and the remainder is 1. Find the smaller number. Solution:                 Let the numbers be x and x+20.                 x+20 = 2x + 1                       x = 19.                The smaller number is 19.                  

Mania Thesaurus: Noun : craze             desire, fascination, fetish, obsession, insanity, madness, lunacy...  Antonyms :  steady, aversion, dislike...  Example sentences:         ·          Sana's mania towards music is unstoppable.  ·        He has a mania  for her.       

Answers of Day 50:               1. 3.               2. 384. Problems on Numbers 1. Two different natural numbers are such that their product is less than their sum. One of the numbers must be: Solution:                 Let one number be x.                 (x*1) < (x+1).                 Hence one of the numbers will be 1. 2. The product of two numbers is 100 and the sum of their squares is 641. What's the sum of two numbers? Solution:                (x+y) 2 = x 2 +y 2 +2xy                           = 641+2(100)                           = 841                      x+y = 29.

Zeal Thesaurus: Noun : enthusiasm              keenness, mania, passion, perseverance, eagerness, interest, hustle...  Antonyms :  apathy, lack of interest... Example sentences:         ·          Her zeal  shows from her behaviour.  ·        She learns everything with a great zeal .        

P roblems to solve 1. The difference between 2 integers is 2 and their product is 15. Find the smaller number. 2. If the sum and the difference of 2 numbers are 32 and 12 respectively, then find the difference of their squares.

Anonymous Thesaurus: Adjective : unknown                     pseudo, secret, nameless, unacknowledged, unclaimed, unidentified...  Antonyms :  named, identified... Example sentences:         ·          He anonymously did good things to the society.  ·        She received anonymous letters.        

                Hey, my friends... How is your life going on? Are my tips working? Please share your feedback so that I can improve myself.                                         It's time to get back to your childhood to know who you really are... Let's dig out deep inside to know about us more. For example, I'll share my experience. This gives you a hint to think about it.                                                                           Then Morning:                                                                                           When I was 13, I used to wake up at 5am and I'll do some cleaning works for 10 minutes after refreshing. I'll do yoga for 30 minutes. After this, I'll take bath and have my coffee by 6am. At sharp 6am, I'll go to the upstairs to study and I'll return downstairs by 8am to get ready for my school and have my breakfast by 8.30 and at sharp 8.30 I'll go by bicycle to my school. Evening:    

Contingency  Thesaurus: Noun : possibility               chance, event, probability, turning point, opportunity, uncertainty...  Antonyms :  certainty, reality... Example sentences:         ·          Is there any contingency to make that happen?  ·        There are numerous   contingencies in the field of Mathematics.       

Problems on Numbers 1. The sum of two numbers is 16. Three times of the first number will be five times of the second number. Find their product. Solution:                Let the 2 numbers are x and y.                x+y = 16    ------ Equation 1                3x = 5y                   x = 5y/3                Substitude x value in equation 1. We get,                5y/3 + y = 16                5y+3y = 16*3                    8y = 16*3                        y = 6.                Then, x = 10.                Their product is 6*10 = 60. 2. The sum of two numbers is 33 and their difference is 3. Find their ratio. Solution:                Let the numbers be x and y.                x+y = 33                x-y = 3                By solving these two equations we get,                2x = 36                 x = 18.                 y = 15.                 Their ratio is 18:15 which is 6:5.

Answer of Day 47:  9 Problems on Numbers 1. Two numbers are such that the ratio between them is 2:9. If each is increased by 3, the ratio becomes 3/10. The smaller number is: Solution:                 (2x+3)/(9x+3) = 3/10                  10(2x+3) = 3(9x+3)                     20x+30 = 27x+9                             7x = 21                               x = 3.                The smaller number is 2(3)= 6. 2.  The sum of three numbers is 27. If the first number is thrice of third number and the second number is half of the third number. What's the third number? Solution:                Let the third number be x.                3x+1/2(x)+x = 27                      6x+x+2x = 27*2                                  9x=27*2                                    x= 6.              The third number is 6.

Munch Thesaurus: Verb : eat audibly           bite, mash, grind, smash, crunch, chew...         Example sentences:         ·         H e   munches on something which makes us turn around.  ·        She munched on her snack while studying.        

Problem On Numbers 1. Three numbers are in the ratio 1:2:3 and their average is 180. What's the largest number? Solution:                 Let the numbers be x, 2x and 3x.                 x+2x+3x = 180                          6x = 180                            x = 30                The largest number is 3x = 90. Problem to solve: Three numbers are in the ratio of 4:2:3 and their product is 648. Find the smallest number. 

Scrutinize Thesaurus: Verb : explore or examine carefully            analyze, check, inspect, investigate, look over, pierce, survey, watch, study...  Antonyms : neglect...        Example sentences:         ·         To find the opportunities, one must scrutinize what's happening around them.  ·        She scrutinized literally everything and found the murderer.        

Answers of Day 45:                                 1. 9/14                                 2. 4 1. The product of 2 natural numbers is 15. Then, the sum of the reciprocals of their squares is: Solution:                 Let the numbers be x and y.                 1/x 2 +1/y 2 = (y 2 +x 2 )/x 2 y 2                                  = (15 2 +1 2 )/(1*15) 2                                  =  (225+1)/225                                  =  226/225. 2. If 3(1/2) is added to a number and that sum is divided by 2(3/5) and the result of this is added to 2/3. This value will be equal to 5. What's that number? Solution:                Let the number be x.                 x+3(1/2)                -------------   +  2/3 = 5                  2(3/5)                   x+7/2                 -------------    +  2/3 = 5                    13/5                  2x+7           5                ---------  *    ----    +   2/3 = 5                     2