Aptitude Discussion

Q. |
$(AA)^2 = DCBA$, where $A$, $B$, $C$ and $D$ are distinct digits with $B$ being odd. Find the value of $D$. |

✔ A. |
4 |

✖ B. |
6 |

✖ C. |
1 |

✖ D. |
1 or 4 |

**Solution:**

Option(**A**) is correct

Check the digits $A =1,2,3,4,......9$

$11 \times 11= 121$ (Not valid, only 3 digit number)

$22 \times 22= 484$ (Not valid, only 3 digit number)

$33 \times 33= 1089$ (Not valid, $B$ is NOT odd)

$44 \times 44= 1936$ (NOT valid since digit $A$ is not $4$ on the ridht hand side - unit's place)

$55 \times 55= 3025$ (Not valid, $B$ is NOT odd)

$66 \times 66= 4356$ (**Valid choice, keep note of it**)

$77 \times 77= 5929$ (Not valid, digits are NOT distinct)

$88 \times 88= 7744$ (Not valid, digits are NOT distinct)

$99 \times 99= 9801$ (Not valid, $B$ is NOT odd)

So we see that, only $66 \times 66= 4356$ satisfy the criteria.

Hence, $D =\textbf{4}$

**Alternative Solution:**

Note that for a perfect square number with ten's place odd, unit's place of the number must be 6.

$66×66 = 4356$.

also $44 \times 44=1936$ B is odd in both the cases.

But in the second case unit's digit on the right hand side is not $4$ ($44 \times 44 = DCB4$). So this option is NOT valid.

Then $D =\textbf{4}$

**P V Ashok**

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Solution has been modified as per your point. Correct answer choice has been pointed out as well.

**Deep**

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As per question , unit digit should be same as the digits multiplied .

if we multiply 44 x 44 , we donot get unit digit as 4 in the solution

Thank you for notifying the anomaly. Solution has been modified.

**Buggi**

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the answer would be A (4)

**Sahil**

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yeah i agree...

'A'whether in left side or in right side both should have same values i.e 6

if u make L.H.S (88*88 or 44*44) then in R.H.S also A will have the same value

i.e 4 or 8

rather it should have been E instead of A on R.h.s then ans then the ans. would have been 1 or 4

**Niket**

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The answer can only be 4 as the case of 66 is valid since the last digit of the answer should be same as the left side i.e A

**Niket**

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the answer can only be 4 since the last digit of the answer Should also be A so only the case of 6 is valid

**Narendra Singh**

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As question says $(AA*AA)=DCBA$ then unit digit must be same i.e. A.

So only 1 solution which would satisfy this equation will be $66*66= 4356$. Here unit digit is same at both place i.e. 6 and 10th digit is Odd so correct answer would be 4.

Option 'A' should be the correct answer.

I think most of the person missed this point.

Please do change in solution which u have provided.

**Robin Dhingra**

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According to me the answer would be all the options because square of $44=1936$ $66=4356$ and $88=6776$ also satisfies the conditions.

So the value of $d$ could be 1 4 or 6 also.

**Ashita**

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According to me the answer to this question must be $D$ ie 1 or 4..

Since square of 44 is 1936 ie $B=3$ and $D=1$

AA*AA should give DCBA 66*66 = 4356.....where does 44*44 give 4 in the unit's digit of answer?