Problems of the day

[Jatin Kr Dey]

1.  How many positive three-digit integers have a remainder of 2 when divided by 6, a remainder of 5 when divided by 9, and a remainder of 7 when divided by 11 ?

(A) 1 (B) 2 (C) 3 (D) 4 (E) 5                       (AMC)

2.

Suppose $$ a ,b ,  and \ c$$ are nonzero real numbers, and $$ a+b+c = 0 $$ . What are the possible value(s) for $$\frac{a}{|a|} + \frac{b}{|b|} + \frac{c}{|c|} + \frac{abc}{|abc|}$$? (A) 0 (B) 1,-1 (C)2,-2 (D)0 , 2 and -2 (E) 0 , 1 and -1  (AMC)

 

[cyberx R3der]

<p style="text-align: left;">1) All number of form 198k+194 leave the desired remanider as given for k>=0. So till k=4 u will get 3 digit numbers.therefore the ans is 5.</p>
<p style="text-align: center;">2)As the sum of 3 nonzero real numbers is 0.All the no. cant be negative or postive.</p>
Case 1: 1 number negative.(assume a) then abc is also negative. Thus u will get +2 for b and c and -2 for a and abc which equates to 0.

Case 2: 2 numbers negative.(assume a and b) . Then abc is postive. Thus u will get +2 for c and abc and -2 for a and b which equates to 0.

Thus the ans is 0.

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