Hi Bhavin,
I guess i made some mistake in approach towards the answer...Rather i took it as Square than Rhombus.....
Explanation goes like this....
ABCD is a Rhombus....
AB=BC=CD ...also =AD....
so AB=BC=CD=AD=r
Take centre of BD as O....
and by Rhombus properties ...AO=OC = AC/2 = r/2 ..
and AOB=COB ...is right angle
so by Pythagoras theorem ...AB^2 = AO^2 + OB^2....
==> r^2 = (r/2)^2 + OB^2...
so OB = root(3)/3....
so tan (x) = AO/OB....(r/2)/(root(3)*r)/2 = 1/root(3)
==> x = tan Inverse (1/root(3)) = 30 degrees....
Correct me if i am wrong...
Originally Posted by msd_2008 View Post
Hello,
Someone please help me with the following question:
Q.1 A circular jogging track forms the edge of a circular lake that has a diameter of 2 miles. Johanna walked once around the track at the average speed of 3 miles per hour. If t represents the number of hours it took Johanna to walk completely around the lake, which of the following is a correct statement?
A. 0.5
B. 1.75
C. 2.0
D. 2.5
E. 3
Thanks
MSD
i guess the correct answer should be D.msd_2008 ,can you please verify
Distance travelled by Johanna = 3t miles = Circumfrence of lake = 2//r
so 3t = 22/7*2
or t = 2.095
So correct answer is choice C
A merchant paid $300 for a shipment of x identical calculators. The merchant used 2 of the calculators as demonstrators and sold each of the others for $5 more than the average (arithmetic mean) cost of the x calculators. If the total revenue from the sale of the calculators was $120 more than the cost of the shipment, how many calculators were in the shipment?
(A) 24
(B) 25
(C) 26
(D) 28
(E) 30
Pl help.....
(A) 24
(B) 25
(C) 26
(D) 28
(E) 30
Pl help.....
A merchant paid $300 for a shipment of x identical calculators. The merchant used 2 of the calculators as demonstrators and sold each of the others for $5 more than the average (arithmetic mean) cost of the x calculators. If the total revenue from the sale of the calculators was $120 more than the cost of the shipment, how many calculators were in the shipment?
(A) 24
(B) 25
(C) 26
(D) 28
(E) 30
Pl help.....
@ashishjha100 -
I hope this will help -
Avg (Arithmetic mean) cost for x calculators = 300/x
Selling price for 1 calculator = (300/x) + 5 (5 more than avg price of calculator)
No. of calculators sold by merchant = x-2 (2 less than no. of calculators bought)
Total revenue from the sale = 300 + 120 = 420
we know that - Total revenue = Selling price for 1 calculator * No. of calculators sold
=> * = 420
After simplifying quadratic equation, you'll get 30 as the answer. Also, you can try putting 30 directly in the above equation.
P.S - I read somewhere that when you need to chose and eliminate the choices, start from E to A.
A merchant paid $300 for a shipment of x identical calculators. The merchant used 2 of the calculators as demonstrators and sold each of the others for $5 more than the average (arithmetic mean) cost of the x calculators. If the total revenue from the sale of the calculators was $120 more than the cost of the shipment, how many calculators were in the shipment?
(A) 24
(B) 25
(C) 26
(D) 28
(E) 30
Pl help.....
avg for x calculators is 300/x.
he sold (x-2) calculators for (300/x+5).
so revenue (x-2)(300/x+5) = 300+20.
it is easy to solve it by substitution rather than solving the equation. one can save some time by substituting lowest and highest (here 24 and 30) and then moving on to next options. after doing with highest and lowest you kind of get the idea which value it could be. this just saves some seconds of your time. 😉
@ashishjha100 -
I hope this will help -
Avg (Arithmetic mean) cost for x calculators = 300/x
Selling price for 1 calculator = (300/x) + 5 (5 more than avg price of calculator)
No. of calculators sold by merchant = x-2 (2 less than no. of calculators bought)
Total revenue from the sale = 300 + 120 = 420
we know that - Total revenue = Selling price for 1 calculator * No. of calculators sold
=> * = 420
After simplifying quadratic equation, you'll get 30 as the answer. Also, you can try putting 30 directly in the above equation.
P.S - I read somewhere that when you need to chose and eliminate the choices, start from E to A.
Thanks Dopa,
I was in a confusion to take 300 as cargo charge or total price of x calculators......
Ya buddy got it........Some calculation mistake .........
thanks a lot for explaining
Originally Posted by Inder.14 View Post
Originally Posted by msd_2008 (GMAT Problem Solving Discussions)
" />"]
Hello,
Someone please help me with the following question:
Q.1 A circular jogging track forms the edge of a circular lake that has a diameter of 2 miles. Johanna walked once around the track at the average speed of 3 miles per hour. If t represents the number of hours it took Johanna to walk completely around the lake, which of the following is a correct statement?
A. 0.5B. 1.75C. 2.0 D. 2.5 E. 3
Thanks
MSD
i guess the correct answer should be D.msd_2008 ,can you please verify
Distance travelled by Johanna = 3t miles = Circumfrence of lake = 2//r" />
so 3t = 22/7*2
or t = 2.095
So correct answer is choice C
Originally Posted by msd_2008 View Post
Hello,
Someone please help me with the following question:
Q.1 A circular jogging track forms the edge of a circular lake that has a diameter of 2 miles. Johanna walked once around the track at the average speed of 3 miles per hour. If t represents the number of hours it took Johanna to walk completely around the lake, which of the following is a correct statement?
A. 0.5
B. 1.75
C. 2.0
D. 2.5
E. 3
Thanks
MSD
i guess the correct answer should be D.msd_2008 ,can you please verify
The correct answer is C.
Need help with the following problem :
Q. How many 5 digit numbers can be formed which are divisible by 3 using the numerals 0,1,2,3,4,5 (WITHOUT REPETITION)
a. 216
b. 3152
c. 240
d. 600
Rgds
MSD
Is the answer (A) - 216?
Need help with the following problem :
Q. How many 5 digit numbers can be formed which are divisible by 3 using the numerals 0,1,2,3,4,5 (WITHOUT REPETITION)
a. 216
b. 3152
c. 240
d. 600
Rgds
MSD
Need help with the following problem :
Q. How many 5 digit numbers can be formed which are divisible by 3 using the numerals 0,1,2,3,4,5 (WITHOUT REPETITION)
a. 216
b. 3152
c. 240
d. 600
Rgds
MSD
My pick is A.
If the ans is correct i'll give reasoning..........
My pick is A.
If the ans is correct i'll give reasoning..........
Yes. The answer is A. can you please provide explanation?
Rgds
MSD
Yes. The answer is A. can you please provide explanation?
Rgds
MSD
By the property of divisibility by 3 ie "a no: is divible by 3, if the sum of the digits is divisible by 3"(eg= 12-->1+2=3)
so from 0,1,2,3,4,5 the set of 5 digit no:s that can be formed which is divisible by 3 are 0,1,2,4,5(sum=12) & 1,2,3,4,5(sum=15)
from first set(0,1,2,4,5) no:s formed are 96 ie first digit can be formed from any 4 no: except 0, second digit from 4 no: except digit used at first place,3rd from rest 3 , 4th from rest 2 no: and in fifth remaining digit since no repetition allowed.
from second set(1,2,3,4,5) no:s formed are 120 ie first digit can be formed from any 5 digits, second digit from 4 no: except digit used at first place,3rd from rest 3 , 4th from rest 2 no: and in fifth remaining digit since no repetition allowed.
so otal 120+96=216
For a number to be divisible by 3, the sum of the digits must be divisible by 3.
Taking 0,1,2,3,4,5 - split this problem into 2 parts
1) take 1,2,3,4,5 alone => we can form 5! five-digit numbers from these digits = 120
2) now taking 0 along with the other 5 digits, we need to ensure two things A) 0 does not start the number and B) the sum is divisible by 3.
so with digits 0,1,2,4,5 (ignore the digit "3" as it does not give us a number divisible by 3) we can form 4x4! numbers = 4 x 24 = 96
summing them up = 120+96 = 216.. hope this helps!
Yes. The answer is A. can you please provide explanation?
Rgds
MSD
Need help with the following problem :
Q. How many 5 digit numbers can be formed which are divisible by 3 using the numerals 0,1,2,3,4,5 (WITHOUT REPETITION)
a. 216
b. 3152
c. 240
d. 600
Rgds
MSD
Here I go>>>.
Differenct combinations of 5 digits out of the six available are---
01234 total = 10
01235 total = 11
01245 total = 12
01345 total = 13
02345 total = 14
12345 total = 15
So in order to be divisible by 3 a combination of five digit must be either (01245) or (12345).
01245 no of arrangements = 4*4*3*2*1 (0 cannot be on the first place) = 96
12345 no of arrangements = 5*4*3*2*1 = 120
Total = 96+120 = 216
Hi...
Could someone help me in solving these problems. I have posted answers along with these. But haven't got a clue on how to arrive at these answers..
1) For every positive integer n, the function h(n) is defined to be the product of all event integers from 2 to n, inclusive. If p is the smallest prime factor of h(100)+1, then p is
(a) between 2 and 10
(b) between 10 and 20
(c) between 20 and 30
(d) between 30 and 40
(e) greater than 40
Ans: e
2) On a certain sight-seeing tour, the ratio of the number of women to the number of children was 5 to 2. What was the number of men on the sight-seeing tour?
(1) On the sight-seeing tour, the ratio of the number of children to the number of men was 5 to 11
(2) The number of women on the sight-seeing tour was less than 30.
Ans (c)
3) If n is a multiple of 5 and n=p^2q, where p and q are prime numbers, which of the following must be a multiple of 25?
(a) p^2
(b) q^2
(c) pq
(d) p^2q^2
(e) p^3q
Ans (d)
4) Of the students who eat in a certain cafeteria, each student either likes or dislikes lima beans and each student either likes or dislikes brussel sprouts. Of these students, 2/3 dislike lima beans; and of those who dislike lima beans, 3/5 also dislike brussel sprouts. How many of teh students like brussels sprouts but dislike lima beans?
(1) 120 students eat in the cafeteria
(2) 40 of the students like lima beans
Ans (D)
5) If each of the following fractions were written as a repeating decimal, which would have the longest sequence of different digits?
(a) 2/11
(b) 1/3
(c) 41/99
(d) 2/3
(e) 23/37
Ans : e
1) For every positive integer n, the function h(n) is defined to be the product of all event integers from 2 to n, inclusive. If p is the smallest prime factor of h(100)+1, then p is
(a) between 2 and 10
(b) between 10 and 20
(c) between 20 and 30
(d) between 30 and 40
(e) greater than 40
Ans: e
h(n) will not include any prime no other than 2, but will include twice of prime nos. So all the nos less than 50 will be the factor of h(n). So, the largest prime factor of h(n) will be less than equal to 50. So the smallest prime factor of h(n) +1 will not less than 50 (will be greater than 50). So the best answer is E.
________________________________________________________________________________________
2) On a certain sight-seeing tour, the ratio of the number of women to the number of children was 5 to 2. What was the number of men on the sight-seeing tour?
(1) On the sight-seeing tour, the ratio of the number of children to the number of men was 5 to 11
(2) The number of women on the sight-seeing tour was less than 30.
Ans (c)
From Question W/C=5/2 M=?
(1) C/M=5/11, W not known so not sufficient so BCE,
(2) W
(1+2) W/C * C/M = W/M=25/22 M=22W/25 As the no of Men is a whole no 22W/25 should be an integer, which means W should be divisible by 25. As W
So the answer is C
________________________________________________________________________________________
3) If n is a multiple of 5 and n=p^2q, where p and q are prime numbers, which of the following must be a multiple of 25?
(a) p^2
(b) q^2
(c) pq
(d) p^2q^2
(e) p^3q
Ans (d)
n=p^2q
or k.5= p^2q
or (k.5)^2= (p^2q)^2
or k^2 * 25=p^2q^2
SO the answer is D
________________________________________________________________________________________
4) Of the students who eat in a certain cafeteria, each student either likes or dislikes lima beans and each student either likes or dislikes brussel sprouts. Of these students, 2/3 dislike lima beans; and of those who dislike lima beans, 3/5 also dislike brussel sprouts. How many of the students like brussels sprouts but dislike lima beans?
(1) 120 students eat in the cafeteria
(2) 40 of the students like lima beans
Ans (D)
From Question stem
Students
Students
Students
From (1) Total Students = 120 Sufficient. (2/5*2/3*120)
From (2) As Students
So Students
So Total Students = 40*3 = 120 Sufficient (2/5*2/3*120)
So Answer is D
___________________________________________________________________________________
5) If each of the following fractions were written as a repeating decimal, which would have the longest sequence of different digits?
(a) 2/11
(b) 1/3
(c) 41/99
(d) 2/3
(e) 23/37
Ans : e
This is based on general properties of numbers.
1/N Where N= 0 to 9
For every digit has its fixed recurring decimal nos.
1/1=1.000000
1/2=0.500000
1/3=0.333333
1/4=0.250000
1/5=0.200000
1/6=0.166666
1/7=0.142857
and so on
It is a clear fact that 7 has the most no recurring decimal places. So every no having 7 as its unit digit will follow the similar pattern.
So the answer is E.
_____________________________________________________________________________________
1. Five pieces of wood have an average (AM)length of 124 cm and a median length of 140 cm. What is the maximum possible length,in cm,of the shortest piece of wood?
a) 90 b) 100 c) 110 d) 130 e) 140
2. For any +ve integer n is defined as the number of prime factors whose product is n. For example, the length of 75 is 3, since 75=3*5*5. How many two-digit +ve intergers have length 6?
a) None b)One c)Two d)three e) Four
Pls post ur answers with explanation...i will post the answers..tomorrow..
My take is
Q1 - Answer (b) = 100
Q2 - Answer (c) = Two
what are the OAs?
1. Five pieces of wood have an average (AM)length of 124 cm and a median length of 140 cm. What is the maximum possible length,in cm,of the shortest piece of wood?
a) 90 b) 100 c) 110 d) 130 e) 140
2. For any +ve integer n is defined as the number of prime factors whose product is n. For example, the length of 75 is 3, since 75=3*5*5. How many two-digit +ve intergers have length 6?
a) None b)One c)Two d)three e) Four
Pls post ur answers with explanation...i will post the answers..tomorrow..
My take is
Originally Posted by Bunty4Billi View Post
1. Five pieces of wood have an average (AM)length of 124 cm and a median length of 140 cm. What is the maximum possible length,in cm,of the shortest piece of wood?
a) 90 b) 100 c) 110 d) 130 e) 140
2. For any +ve integer n is defined as the number of prime factors whose product is n. For example, the length of 75 is 3, since 75=3*5*5. How many two-digit +ve intergers have length 6?
a) None b)One c)Two d)three e) Four
Pls post ur answers with explanation...i will post the answers..tomorrow..
Q1 - Answer (b) = 100
Q2 - Answer (c) = Two
what are the OAs?
i guess the answer for first one should be (a) i.e 90
Need help with the following data sufficiency problem. Plz provide explanation.
Q. In a xy plane, region R consists of all the points (x,y) such that 2x+3y=6. Is the point (r,s) in region R?
1. 3r+2s=6
2. r=3 and s=2
Rgds
MSD