GMAT Problem Solving Discussions

MBA
1469
It takes machine A x hours to manufacture a deck of cards that machine B can manufacture in 1/x hours. If machine A operates alone for y hours and is then joined by machine B until 100 decks are finished, for how long will the two machines operate simultaneously?

(100y - x)

(x2 + 1)

(100x - y)

(x2 + 1)

(100y - x3 - x)

(x2 + 1)

(100y - x2y - y)

(x2 + 1)

(100x)

(x2 + 1)

Note:- x2 = x^2; x3 = x^3; x2y = (x^2)*y










Is it E........
1470
ashishjha100 Says
Is it E........

It is E as machines A & B work simulataneously worked only to complete 100 decksof cards.

In i hr A and B do (1/x+x)= (x^2+1)/x
Hence x/(x^2+1) decks are completed in 1 hr
To complete 100 decks, they wud take 100x(x^2+1)

The ques here is for howl long do two machines work together and its clearly for 100 decks of cards.
1472
The OA is (B)

Originally Posted by *arch* View Post
It takes machine A x hours to manufacture a deck of cards that machine B can manufacture in 1/x hours. If machine A operates alone for y hours and is then joined by machine B until 100 decks are finished, for how long will the two machines operate simultaneously?

(100y - x)

(x2 + 1)

(100x - y)

(x2 + 1)

(100y - x3 - x)

(x2 + 1)

(100y - x2y - y)

(x2 + 1)

(100x)

(x2 + 1)

Note:- x2 = x^2; x3 = x^3; x2y = (x^2)*y
1473

In 1 hour A manufactures 1/x deck
In 1 hour B manufactures x deck

Hence in one hour A and B combined : (1/x + x) deck

A in y hours : y/x deck
Off 100 decks , remaining decks = (100-y/x)

Hence time need by A and B to manufacture remaining deck :

(100 - y/x) / (1/x+x)

Simplify this and answer is B

1474

i have 2 questions from gmat prep..
1)If x A)-x
B)-1
C)1
D)x
E)sqroot(x)

here the official answer is A but i feel its D.. please explain.
2) In may Mrs. Lee's earnings were 60 percent of the lee family's total income. In june Mrs. Lee earned 20 percent earned more than in may. if the rest of the family's income was the same both months, then, in june, Mrs. Lee's earnings were approximately what percent of the lee family's income?
A) 64%
B) 68%
C) 72%
D) 76%
E) 80%

Here the official answer is A but i feel its C.. please explain.
thanks in advance
Regards,
Manish

1475
i have 2 questions from gmat prep..
1)If xA)-x
B)-1
C)1
D)x
E)sqroot(x)

here the official answer is A but i feel its D.. please explain.
2) In may Mrs. Lee's earnings were 60 percent of the lee family's total income. In june Mrs. Lee earned 20 percent earned more than in may. if the rest of the family's income was the same both months, then, in june, Mrs. Lee's earnings were approximately what percent of the lee family's income?
A) 64%
B) 68%
C) 72%
D) 76%
E) 80%

Here the official answer is A but i feel its C.. please explain.
thanks in advance
Regards,
Manish



for question number 1)
answer will be A i.e -x
Explanation:
xlets assume x = -a

sqrt(-xx|)=sqrt(-(-a)-a)=sqrt(a*a)=a =-x

hope you got it.

and for second question i too think it should be c i.e 72%
1476
i have 2 questions from gmat prep..
1)If x A)-x
B)-1
C)1
D)x
E)sqroot(x)

here the official answer is A but i feel its D.. please explain.
2) In may Mrs. Lee's earnings were 60 percent of the lee family's total income. In june Mrs. Lee earned 20 percent earned more than in may. if the rest of the family's income was the same both months, then, in june, Mrs. Lee's earnings were approximately what percent of the lee family's income?
A) 64%
B) 68%
C) 72%
D) 76%
E) 80%

Here the official answer is A but i feel its C.. please explain.
thanks in advance
Regards,
Manish

Q2) Let lee family's income in may be x
Mrs Lee earns in may = 0.6x
Rest of family's income = 0.4x
Mrs Lee's income in june = 0.72 x
Rest of family's incomein june = 0.4x
Hence % of Mrs lee's income to that of entire family = 0.72x/(0.72x+0.4x) = 64% approx
Hence OA is A

q1) Let x=-3(since xsqrt (-xIxI) = sqrt (4) = +/-2 or +/-x

dear inder ideviate frm ur last line whereu said sqrt (a*a) = a...it cud be -a as well
dear manish, while posting questions do not post the OA along with the ques...let everyone on PG give it a try.

thanks
1477
Q2) Let lee family's income in may be x
Mrs Lee earns in may = 0.6x
Rest of family's income = 0.4x
Mrs Lee's income in june = 0.72 x
Rest of family's incomein june = 0.4x
Hence % of Mrs lee's income to that of entire family = 0.72x/(0.72x+0.4x) = 64% approx
Hence OA is A

q1) Let x=-3(since xsqrt (-xIxI) = sqrt (4) = +/-2 or +/-x

dear inder ideviate frm ur last line whereu said sqrt (a*a) = a...it cud be -a as well
dear manish, while posting questions do not post the OA along with the ques...let everyone on PG give it a try.

thanks

in continuation to my above post i'm not clear whether the OA is A or D.

pl help guys

thanks
1478

Question (1) --> sqrt(-x x|)

as x
Sqrt(x^2) has to be -x;

This is because --> the answer choices indicate that the sqrt in this case is positive (as no choice has an imaginary (i) component in it).

So, since we have been given that xto ensure that the sqrt is positive.

if you choose "x" as the answer, that would imply that the sqrt is an imaginary number.. which is definitely not the case here!

in continuation to my above post i'm not clear whether the OA is A or D.

pl help guys

thanks
1479
Ans1)
To explain this using an example, let's take x = -2

then we have 2 options for sq root (-xx|)

first when x| = -2 and other when |x = 2

The first one gives: sq root (-4) which is an imaginary number, therefore not a solution.

The second option gives: sq root(4) = 2

Therefore we get the answer as,

sq root (-x|x) = -x (we started with x = -2 but ended with 2 therefore the answer is -x)

Ans2)
The answer should be 64%. Those who are saying 72% are not taking into consideration the line "the rest of the family's income was the same both months"
1480
@ arch -
As x sqrt(-x x) = sqrt(2 |-2) = sqrt(4) = +2 OR -2

Answer choices didn't say anything about imaginary root, imaginary roots will only come into picture when we have to calculate sqrt(-4) but here the case is sqrt(4)

@ Tapas -
How can |x = -2 is possible, mod of any value will always be positive.

@ itsagarwal - Whats the explanation given in Gmatprep for this question ?

I think , it can be +/-x, so answer can't be A. But as the OA given is A, there should be some other reason behind the answer, PUYS please try to put other reasoning.
1481
@ Dopa -
(this is what i meant..)

As x sqrt(-x x) = sqrt(2 -2) = sqrt(2*2) = +2
+2 = -(-2) = -x

Plz correct me if i'm wrong.
@ arch -
As x sqrt(-x x) = sqrt(2 |-2) = sqrt(4) = +2 OR -2

Answer choices didn't say anything about imaginary root, imaginary roots will only come into picture when we have to calculate sqrt(-4) but here the case is sqrt(4)

@ Tapas -
How can |x = -2 is possible, mod of any value will always be positive.

@ itsagarwal - Whats the explanation given in Gmatprep for this question ?

I think , it can be +/-x, so answer can't be A. But as the OA given is A, there should be some other reason behind the answer, PUYS please try to put other reasoning.
1482

Dopa,
My mistake! I was going by the definition of x and made wrong interpretations. Thanks for correcting me.

I agree that there are 2 possible answers for this quest and imaginary root question will not arise once it's given that x
Thanks!
Tapas

1483
@ Dopa -
(this is what i meant..)

As x sqrt(-x x) = sqrt(2 -2) = sqrt(2*2) = +2
+2 = -(-2) = -x

Plz correct me if i'm wrong.


You are totally correct in your explanation, I have only doubt -

where you mentioned - sqrt(2*2) = +2

I am thinking why is the sqrt(4) = -2 not possible ? because (-2)^2 = 4

May be I am missing some thing really basic. May be GMAC has the same logic as yours.
1484

hi Dopa,

I was wrong is saying x = -2. It's wrong because modulus can never be negative (as you had said). I got confused with the definition of y=|x, which on expansion becomes:

y = x when x>0 or,
y = -x when x
By this definition of |x, y always remains positive.

I do not know what logic GMAC has used but I am trying to find it's solution. There has to ba a catch.

Thanks!
Tapas

1485
@ Dopa

Yeah.. i get what you mean. It's indeed quite confusing here.. but i couldn't think of any logical and straightforward way by which we can get the answer as -x.

I assume GMAC would've reached the answer in the way i mentioned earlier. Otherwise the question is very ambiguous.

sqrt (-x x) --> becomes sqrt (2*2) = so we simply take sqrt (2*2) = +2 which is -(-2) = -x.

You are totally correct in your explanation, I have only doubt -

where you mentioned - sqrt(2*2) = +2

I am thinking why is the sqrt(4) = -2 not possible ? because (-2)^2 = 4

May be I am missing some thing really basic. May be GMAC has the same logic as yours.
1486

If y intercept is 6 and slope of a line is 3 ,then x intercept is..........

I have this basic doubt......pls help

1487
If y intercept is 6 and slope of a line is 3 ,then x intercept is..........

I have this basic doubt......pls help

general equation of a line having slope m is y = mx + c

Y intercept is 6 i.e. at that point x = 0, putting it in above equation gives -> c = 6.

So, now the equation can be written as y = 3x + 6.

For calculating x intercept, put y = 0 => 3x + 6 = 0 => x = -2.
Hence, x intercept = -2

Hope it helps...
1488

Each side of a certain parallelogram has length 6. if the area of the parallelogram is 18.
which of the following is the measure of one of its angles?
A. 30' B. 45' C. 60' D. 90' E.120'

1489

A small square is inscribed in a large square.What is the perimeter of larger square?(measurements given are3 & 4):sarcasm: