GMAT Problem Solving Discussions

tikna_atpug · October 17, 2009, 10:52pm

In the xy-plane, the point (-2, -3) is the center of a circle. The point (-2, 1) lies inside the circle and the point (4, -3) lies outside the circle. If the radius r of the circle is an integer, then r =
A. 6
B. 5
C. 4
D. 3
E. 2.

IMO: B
Pretty easy one though.

Cheers.
Ankit.

deepakraam · October 18, 2009, 4:43am

In the xy-plane, the point (-2, -3) is the center of a circle. The point (-2, 1) lies inside the circle and the point (4, -3) lies outside the circle. If the radius r of the circle is an integer, then r =
A. 6
B. 5
C. 4
D. 3
E. 2.

Let , A(-2,1) B(-2,-3) & C (4,-3).

Distance (AB) = 4
Distance (BC) = 6.

Radius must lie in between these distances.So only value satisfying the above condition is 5

I will go with option B

neelgandham · October 18, 2009, 6:39pm

In the xy-plane, the point (-2, -3) is the center of a circle. The point (-2, 1) lies inside the circle and the point (4, -3) lies outside the circle. If the radius r of the circle is an integer, then r =
A. 6
B. 5
C. 4
D. 3
E. 2.

Ans : B bery bery veezee

quest0012 · October 18, 2009, 7:41pm

The answer is "E"

quest0012 · October 18, 2009, 7:44pm

A jar contains 30 marbles, of which 20 are red and 10 are blue. If 9 of the marbles are removed, how many of the marbles left in the jar are red?

(1) Of the marbles removed, the ratio of the number of red ones to the number of blue ones is 2 : 1.
(2) Of the first 6 marbles removed, 4 are red.

A Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
B Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.
C BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
D EACH Statement ALONE is sufficient.
E Statements (1) and (2) TOGETHER are NOT sufficient.

ANS) A...very easy

shalinikrishna2 · October 19, 2009, 1:49am

Please answer with explanation.

A box has 6 red hats and 5 green hats. What is the probability of drawing at least one green hat in two consecutive drawings if the hat is not replaced?

a. 10/11

b. 8/11
c.7/12
d.5/13
e.2/7

tikna_atpug · October 19, 2009, 3:17am

Please answer with explanation.

A box has 6 red hats and 5 green hats. What is the probability of drawing at least one green hat in two consecutive drawings if the hat is not replaced?

a. 10/11

b. 8/11
c.7/12
d.5/13
e.2/7

IMO: B

Explanation:
probability of drawing at least one green hat = 1 - probability of drawing no green hat

probability of drawing no green hat = probability of drawing only red hats = (6/11)*(5/10) = 3/11

Hence, Ans = 1 - 3/11 = 8/11

Cheers.

shalinikrishna2 · October 19, 2009, 6:34am

thanks...it was quite easy to understand like this.

shalinikrishna2 · October 19, 2009, 8:13am

If function $f(x)$ satisfies $f(x) = f(x^2)$ for all $x$ , which of the following must be true?

$f(4) = f(2)f(2)$
$f(16) - f(-2) = 0$
$f(-2) f(4) = 0$
$f(3) = 3f(3)$
$f(0) = 0$

shalinikrishna2 · October 19, 2009, 8:30am

Please answer with explanation...

Some part of a 50% solution of acid was replaced with an equal amount of 30% solution of acid. If, as a result, 40% solution of acid was obtained, what part of the original solution was replaced?

$\frac{1}{5}$
$\frac{1}{4}$
$\frac{1}{2}$
$\frac{3}{4}$
$\frac{4}{5}$

asterixmatrix · October 19, 2009, 9:02am

Please answer with explanation...

Some part of a 50% solution of acid was replaced with an equal amount of 30% solution of acid. If, as a result, 40% solution of acid was obtained, what part of the original solution was replaced?

$\frac{1}{5}$
$\frac{1}{4}$
$\frac{1}{2}$
$\frac{3}{4}$
$\frac{4}{5}$

option 3 - 1/2. considering that the final solution (40%) is average of 50% and 30% so equal amount will be needed of 50% and 30% solution respectively

deepakraam · October 19, 2009, 11:29am

Please answer with explanation...

Some part of a 50% solution of acid was replaced with an equal amount of 30% solution of acid. If, as a result, 40% solution of acid was obtained, what part of the original solution was replaced?

$\frac{1}{5}$
$\frac{1}{4}$
$\frac{1}{2}$
$\frac{3}{4}$
$\frac{4}{5}$

I will go with option 3)1/2

deepakraam · October 19, 2009, 11:30am

If function $f(x)$ satisfies $f(x) = f(x^2)$ for all $x$ , which of the following must be true?

$f(4) = f(2)f(2)$
$f(16) - f(-2) = 0$
$f(-2) f(4) = 0$
$f(3) = 3f(3)$
$f(0) = 0$

I will go with option 2) f(16) - f(2) = 0

neelgandham · October 19, 2009, 11:31am

If function $f(x)$ satisfies $f(x) = f(x^2)$ for all $x$ , which of the following must be true?

$f(4) = f(2)f(2)$
$f(16) - f(-2) = 0$
$f(-2) f(4) = 0$
$f(3) = 3f(3)$
$f(0) = 0$

$f(16) - f(-2) = 0$ is the answer ,

coz f(-2) = f(-2 * -2) = f (4)

then f(4) = f(4*4) = f(6)

so f(16)-f(-2) = 0

correct me if i am wrong !!

neelgandham · October 19, 2009, 11:37am

Please answer with explanation...

Some part of a 50% solution of acid was replaced with an equal amount of 30% solution of acid. If, as a result, 40% solution of acid was obtained, what part of the original solution was replaced?

$\frac{1}{5}$
$\frac{1}{4}$
$\frac{1}{2}$
$\frac{3}{4}$
$\frac{4}{5}$

(0.5 * x + 0.3 (1-x))/1 = 0.4

0.2 *x = 0.1

x = 1\2

trapezio · October 21, 2009, 7:10pm

If function $f(x)$ satisfies $f(x) = f(x^2)$ for all $x$ , which of the following must be true?

$f(4) = f(2)f(2)$
$f(16) - f(-2) = 0$
$f(-2) f(4) = 0$
$f(3) = 3f(3)$
$f(0) = 0$

A) F(4) = F(2) - wrong
B)F(16) = F(4) (or F(-4); not relevant) = F(-2) (or F(2); not relevant)
Hence F(16) = F(-2)
B is the answer

I wouldn't check the rest. 😃

vpitc · October 21, 2009, 11:41pm

The sum of the even numbers between 1 and n is 79*80, where n is an odd number, then n=?
Sol: First term a=2, common difference d=2 since even number
therefore sum to first n numbers of Arithmetic progression would be
n/2(2a+(n-1)d)
= n/2(2*2+(n-1)*2)=n(n+1) and this is equal to 79*80
therefore n=79 which is odd...
Guys,
I think the soln should be 79*2+1=159 am i right?

asterixmatrix · October 21, 2009, 11:47pm

The sum of the even numbers between 1 and n is 79*80, where n is an odd number, then n=?
Sol: First term a=2, common difference d=2 since even number
therefore sum to first n numbers of Arithmetic progression would be
n/2(2a+(n-1)d)
= n/2(2*2+(n-1)*2)=n(n+1) and this is equal to 79*80
therefore n=79 which is odd...
Guys,
I think the soln should be 79*2+1=159 am i right?

yes...n should be 159

vpitc · October 22, 2009, 7:29pm

Guys,
Try this one

The price of a bushel of corn is currently $3.20, and the price of a peck of wheat is $5.80. The price of corn is increasing at a constant rate of 5x cents per day while the price of wheat is decreasing at a constant rate of 0.414x cents per day. What is the approximate price when a bushel of corn costs the same amount as a peck of wheat?
(A) $4.50
(B) $5.10
(C) $5.30
(D) $5.50
(E) $5.60

neha.visionary · October 22, 2009, 7:53pm

Guys,
Try this one

The price of a bushel of corn is currently $3.20, and the price of a peck of wheat is $5.80. The price of corn is increasing at a constant rate of 5x cents per day while the price of wheat is decreasing at a constant rate of 0.414x cents per day. What is the approximate price when a bushel of corn costs the same amount as a peck of wheat?
(A) $4.50
(B) $5.10
(C) $5.30
(D) $5.50
(E) $5.60

$1=100 cents
$3.20= 320 cents
$5.80= 580 cents

Now,as per the ques:
320+5x=580-0.414x
On solving we get x=48.03
Put this value in 320+5(48.03)=560.15 cents or $5.60
Similarily, 580-0.414(48.03)=560.11 cents or $5.60

Hence Answer is E.

Regards,
Neha