Cryptarithmetic








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Quiz Begins Here

Q #1
:

Directions: In this Question , Each Alphabet used is for a distinct digit & the equation given is mathematically true .

Here TEND & BORE are 4- digit numbers & BONEY is a 5-digit number. TEND+BORE=BONEY. What is the value of B+O+N+E+Y?

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Explanation: Two digit maximum addition is (9+9) 18, Since carry is there as letter B. Therefore B has to be 1(B =1). Now T+B has to be greater than 10(it can be 10, 11, 12,...18).Since B=1 T+B will not exceed greater than 11 including carry on T (0 or 1). Therefore O=0 Now to get carry as 1, T must be either 9 or 8, but carry may be there on T (0 or 1). Now E+O (Since O=0) will come E, but we want it different. Therefore on E there is carry as 1. Now N+R must be greater than 10, Therefore (carry (0 or 1) + N+R) =E Carry+E+1+R=E. Therefore R=8 And T must be then 9. D+E greater than 10 Therefore D=7 and E=5, and N=E+1=6, and y=2 Therefore B=1, O=0, N=6, E=5, Y=2. Therefore, B+O+N+E+Y = 1+0+6+5+2 = 14

Q #2
:

Directions: In this Question , Each Alphabet used is for a distinct digit & the equation given is mathematically true .

Here TEND & BORE are 4- digit numbers & BONEY is a 5-digit number . TEND+BORE=BONEY. What is the value of N + E + R – D

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Explanation: Two digit maximum addition is (9+9) 18, Since carry is there as letter B. Therefore B has to be 1(B =1). Now T+B has to be greater than 10(it can be 10, 11, 12,...18).Since B=1 T+B will not exceed greater than 11 including carry on T (0 or 1). Therefore O=0 Now to get carry as 1, T must be either 9 or 8, but carry may be there on T (0 or 1). Now E+O (Since O=0) will come E, but we want it different. Therefore on E there is carry as 1. Now N+R must be greater than 10, Therefore (carry (0 or 1) + N+R) =E Carry+E+1+R=E. Therefore R=8 And T must be then 9. D+E greater than 10 Therefore D=7 and E=5, and N=E+1=6, and y=2 Therefore B=1, O=0, N=6, E=5, Y=2.

Q #3
:

Directions: In this Question , Each Alphabet used is for a distinct digit & the equation given is mathematically true .

Here TEND & BORE are 4- digit numbers & BONEY is a 5-digit number . TEND+BORE=BONEY. What is the value of TO + BO - RO

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Explanation: Two digit maximum addition is (9+9) 18, Since carry is there as letter B. Therefore B has to be 1(B =1). Now T+B has to be greater than 10(it can be 10, 11, 12,...18).Since B=1 T+B will not exceed greater than 11 including carry on T (0 or 1). Therefore O=0 Now to get carry as 1, T must be either 9 or 8, but carry may be there on T (0 or 1). Now E+O (Since O=0) will come E, but we want it different. Therefore on E there is carry as 1. Now N+R must be greater than 10, Therefore (carry (0 or 1) + N+R) =E Carry+E+1+R=E. Therefore R=8 And T must be then 9. D+E greater than 10 Therefore D=7 and E=5, and N=E+1=6, and y=2 Therefore B=1, O=0, N=6, E=5, Y=2.

Q #4
:

Directions: In this Question , Each Alphabet used is for a distinct digit & the equation given is mathematically true .

Here TEND & BORE are 4- digit numbers & BONEY is a 5-digit number . TEND+BORE=BONEY. What is the value of R*O+T- Y

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Explanation: Two digit maximum addition is (9+9) 18, Since carry is there as letter B. Therefore B has to be 1(B =1). Now T+B has to be greater than 10(it can be 10, 11, 12,...18).Since B=1 T+B will not exceed greater than 11 including carry on T (0 or 1). Therefore O=0 Now to get carry as 1, T must be either 9 or 8, but carry may be there on T (0 or 1). Now E+O (Since O=0) will come E, but we want it different. Therefore on E there is carry as 1. Now N+R must be greater than 10, Therefore (carry (0 or 1) + N+R) =E Carry+E+1+R=E. Therefore R=8 And T must be then 9. D+E greater than 10 Therefore D=7 and E=5, and N=E+1=6, and y=2 Therefore B=1, O=0, N=6, E=5, Y=2. Therefore, B+O+N+E+Y = 1+0+6+5+2 = 14

Q #5
:

Directions: In this Question , Each Alphabet used is for a distinct digit & the equation given is mathematically true .

Here TEND & BORE are 4- digit numbers & BONEY is a 5-digit number . TEND+BORE=BONEY. What is the value of R+O+N+E- Y?

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Explanation: Two digit maximum addition is (9+9) 18, Since carry is there as letter B. Therefore B has to be 1(B =1). Now T+B has to be greater than 10(it can be 10, 11, 12,...18).Since B=1 T+B will not exceed greater than 11 including carry on T (0 or 1). Therefore O=0 Now to get carry as 1, T must be either 9 or 8, but carry may be there on T (0 or 1). Now E+O (Since O=0) will come E, but we want it different. Therefore on E there is carry as 1. Now N+R must be greater than 10, Therefore (carry (0 or 1) + N+R) =E Carry+E+1+R=E. Therefore R=8 And T must be then 9. D+E greater than 10 Therefore D=7 and E=5, and N=E+1=6, and y=2 Therefore B=1, O=0, N=6, E=5, Y=2. Therefore, B+O+N+E+Y = 1+0+6+5+2 = 14