# Can someone answer these math questions?! Test of Genius worksheet.?

(1) Make this equation correct by changing the position of only one digit.

101-102=1

(2) Steven has 9 gold coins that are identical in appearance. However, one coin is counterfeit and weighs slightly less than the others. Using a balance scale, how can he find the counterfeit coin inn just two weighings?

(3) In the following addition problem, the letters A,B,and C stand for three different digits. What digit should replace each letter?

ABC

+ ACB

————-

CBA

(4) The teacher noticed there were fewer than 100 students on the playground. When she counted them by 2s, there was 1 student left over. In fact, when she counted them by 3s, 4s, 5s, or 6s, there was always 1 student left over. How many students were on the playground?

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(1) The question says nothing about the operators: 12-011=01

(2) Put 3 of the coins on each side of the scale. If it balances, the counterfeit coin is not on the scale. If it does not balance, the counterfeit coin is on the higher side of the scale.

Put one of the set of three with the counterfeit on each side of the scale. If it balances, the counterfeit coin is not on the scale. If it does not balance, the counterfeit coin is on the higher side of the scale.

(3) From the given equation we know that

C + B = A mod 10

B + C + x = B mod 10

A + A + y = C

where x & y are either 0 or 1 which is the carry over.

Now the first two equations become:

B + C = A mod 10 and

B + C + x = B mod 10

It follows that A = B - x

Since we know we have three DIFFERENT digits,

x must be 1 because A can not be equal to B.

Therefore B = A + 1

(4) Least Common Multiple (LCM) of 2, 3, 4, 5 & 6 plus 1.

I hope that is helpful to you.

Ans (2) let the coins be named as A,B,C,D,E,F,G,H,I

Make three sets set -1:A,B,C, set-2: D,E,F & set-3:G,H,I

Now put set-1 & set-2 on balance scale,

1. if both are equal, the the counterfeit coin is in set-3,

now, put G and H on balance, if both are same then the faulty coin is I

otherwise the faulty coin will weigh less.

2. if both set-1 & set-2 are not equal, then choose the set which is less in weight.

from that put any two coins on balance.

3. if both are equal in weight, then the 3rd one is faulty, otherwise faulty coin will weigh less.

1) 101-10²=1