**Sumer's Doubts with solutions...**

P1:

g^2<1

-1

I know that the sign changes in inequalities when we multiply with –ve sign but if we solve the

above problem as

g^2-1<0

(g+1)(g-1)<0

g<-1 and g<1

Please explain where i’m making a mistake.

**(g+1)(g-1)<0 means -1**

P2:

Q-13, Pg-34, Math-Stage I

P is a multiple of 7 then it should give a different answer every time but answer is A

P3: from Number System I introduction question

83^3743^742

I think answer should be 9 because 3 has a cyclicity of 4 and 3743/4 = 3 and 3^3= 7 and 7^742

gives 2 as remainder and answer should be 9. But right answer is 3 please explain.

P4:

Pg-61,62, math stage I

Q- Maximum/Minimum

When we try to solve the below question with similar approach it does not work

Q-In an office where working in at least one department is mandatory, 78% of the employees are

in operations, 69% are in finance and 87% are in HR. What are the maximum percentage of

employees that could have been working in all three departments?

If I take 69% as the max then the total becomes more than 100% please explain.

**The concept has been explained in great detail in the Algebra video; please watch it again.**P2:

Q-13, Pg-34, Math-Stage I

P is a multiple of 7 then it should give a different answer every time but answer is A

**You're right; we need to get this corrected in the material. We've made a note of this; thanks for bringing this to our notice.**P3: from Number System I introduction question

83^3743^742

I think answer should be 9 because 3 has a cyclicity of 4 and 3743/4 = 3 and 3^3= 7 and 7^742

gives 2 as remainder and answer should be 9. But right answer is 3 please explain.

**The mistake you're committing is in dividing just 3743 by 4 and not 3743^742 by 4. Think, 3%4 = 3 but 3^2%4=1; the power matters****While finding the remainder, divide the entire power by 4****(3743^742)%4****=(3740+3)^742%4****=3^742%4****= 9^371%4****=1^171%4 = 1****Now, 3^1 = 3 remainder.****Don't worry much if you don;t get it; this just a teaser, beyond the GMAT levels.**P4:

Pg-61,62, math stage I

Q- Maximum/Minimum

When we try to solve the below question with similar approach it does not work

Q-In an office where working in at least one department is mandatory, 78% of the employees are

in operations, 69% are in finance and 87% are in HR. What are the maximum percentage of

employees that could have been working in all three departments?

If I take 69% as the max then the total becomes more than 100% please explain.

**Please watch the video carefully; the maximum is simply the smallest of all values; the answer to this question is simple 69% as that's the lowest of the three values.**

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