1. If x is a negative integer, which of the following expression has the least value?
a. X^2  0.5
b. X^2  0.51
c. X^3  0.502
d. X^3  0.511
e. X^4  0.512
2. If n is a multiple of 5 and n = p^2q, where p and q are prime numbers, which of the following will be a multiple of 25?
a. P^2
b. Q^2
c. Pq
d. P^2q^2
e. P^3q
3. A thin piece of wire 40 meters long is cut into two pieces. One piece is used to form a circle with radius r, and the other is used to form a square. No wire is left over. Which of the following is represents the total area, in square meters, of the circular and square regions in terms of r?
a. Pi r^2
b. Pi r^2 +10
c. Pi r^2 + Â¼ Pi^2 r^2
d. Pi r^2 + (40 2Pir)^2
e. Pi r^2 + (10 Â½ Pi r)^2
4. For which of the following functions is F(a+b) = F(a) + F(b) for all positive value of a and b?
a. F(x) = x^2
b. F(x) = x + 1
c. F(x) = SQRT (x)
d. F(x) = 2/x
e. F(x) = 3x
5. From a bag containing 12 identical blue balls Y identical yellow balls, and no other balls, one ball will be removed at random. If the probability is less than 2/5 that the removed ball will be blue, what is the least number of yellow balls that must be in the bag?
a. 17
b. 18
c. 19
d. 20
e. 21
6. If each term in in the sum a1 + a2 +....+ an is either 7 or 77 and the sum equals 350, which of the following could be n?
a.38
b.39
c.40.
d41.
e.42
Algebra and probability
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x<0, find the least value?
x=1
a. 10.5=0.5
b. 10.51=0.49
c. 10.502=1,502
d. 10.511=1,511
e. 10.512=0.abc
IOM d
x=1
a. 10.5=0.5
b. 10.51=0.49
c. 10.502=1,502
d. 10.511=1,511
e. 10.512=0.abc
IOM d
Tagne wrote:1. If x is a negative integer, which of the following expression has the least value?
a. X^2  0.5
b. X^2  0.51
c. X^3  0.502
d. X^3  0.511
e. X^4  0.512
My knowledge frontiers came to evolve the GMATPill's methods  the credited study means to boost the Verbal competence. I really like their videos, especially for RC, CR and SC. You do check their study methods at https://www.gmatpill.com

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n/5 =i (i is integer), n=p^2q {p,q are primes}. Find multiple (M) of 25 <> M/25?
(p^2q)/5 offers the only condition when p=5, So [(5^2)^q]/5 <> (25^q)/5. Q can be anything here ...
a. p^2 Correct, since p=5
b. q^2 Not Correct, as Q can be anything here
c. PQ Not Correct as Q could be 3
d. ...
e ...
IOM A
(p^2q)/5 offers the only condition when p=5, So [(5^2)^q]/5 <> (25^q)/5. Q can be anything here ...
a. p^2 Correct, since p=5
b. q^2 Not Correct, as Q can be anything here
c. PQ Not Correct as Q could be 3
d. ...
e ...
IOM A
Tagne wrote: 2. If n is a multiple of 5 and n = p^2q, where p and q are prime numbers, which of the following will be a multiple of 25?
a. P^2
b. Q^2
c. Pq
d. P^2q^2
e. P^3q
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W (wire) =40, C (circle) =2pi*r (r is radius), S (square) = 4a (a is square side). Find (square S) + (square C) ?
2pi*r+4a=40, a=(402pi*r)/4, a=10 pi*r/2
Square of S = a^2
Square of C= pi*r^2
a^2 + pi*r^2 = (10  pi*r/2)^2 + pi*r^2
IOM E
2pi*r+4a=40, a=(402pi*r)/4, a=10 pi*r/2
Square of S = a^2
Square of C= pi*r^2
a^2 + pi*r^2 = (10  pi*r/2)^2 + pi*r^2
IOM E
Tagne wrote: 3. A thin piece of wire 40 meters long is cut into two pieces. One piece is used to form a circle with radius r, and the other is used to form a square. No wire is left over. Which of the following is represents the total area, in square meters, of the circular and square regions in terms of r?
a. Pi r^2
b. Pi r^2 +10
c. Pi r^2 + Â¼ Pi^2 r^2
d. Pi r^2 + (40 2Pir)^2
e. Pi r^2 + (10 Â½ Pi r)^2
My knowledge frontiers came to evolve the GMATPill's methods  the credited study means to boost the Verbal competence. I really like their videos, especially for RC, CR and SC. You do check their study methods at https://www.gmatpill.com

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a. (a+b)^2=a^2+b^2 Not Correct;
b. a+b+1=a+1 + b+1 Not Correct;
c. Sqrt (a+b) = Sqrt(a) +Sqrt(b) Not Correct;
d. 2/(a+b) =2/a +2/b Not Correct;
e. 3(a+b) = 3a + (3b) Correct.
IOM E
b. a+b+1=a+1 + b+1 Not Correct;
c. Sqrt (a+b) = Sqrt(a) +Sqrt(b) Not Correct;
d. 2/(a+b) =2/a +2/b Not Correct;
e. 3(a+b) = 3a + (3b) Correct.
IOM E
Tagne wrote:4. For which of the following functions is F(a+b) = F(a) + F(b) for all positive value of a and b?
a. F(x) = x^2
b. F(x) = x + 1
c. F(x) = SQRT (x)
d. F(x) = 2/x
e. F(x) = 3x
My knowledge frontiers came to evolve the GMATPill's methods  the credited study means to boost the Verbal competence. I really like their videos, especially for RC, CR and SC. You do check their study methods at https://www.gmatpill.com

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this problem is missing critical part i put in red
P(blue)<2/5. Find the least number of yellow balls?
The question says that less than (2/5) of (12 blue balls+ x yellow balls) in the bag are blue balls  OR, 12/(12+x) <2/5, 60<24+2x, 36<2x and x>13
Let's check the question again :"what is the least number of yellow balls that must be in the bag?"
answer choice A seems fitting
IOM A
we can have one 77 and (5011) 7s (sevens) OR total 40 numbers
two 77s and (5022) 7s OR total 29 numbers
and so on with the numbers (n) decreasing, it's evident that n=40
IOM C
P(blue)<2/5. Find the least number of yellow balls?
The question says that less than (2/5) of (12 blue balls+ x yellow balls) in the bag are blue balls  OR, 12/(12+x) <2/5, 60<24+2x, 36<2x and x>13
Let's check the question again :"what is the least number of yellow balls that must be in the bag?"
answer choice A seems fitting
IOM A
all numbers can be factored by 7 > 350/7=50. Now we have 50 7s and the 7s (sevens) must be associated with 77.Tagne wrote: 5. From a bag containing 12 identical blue balls, certain number of yellow balls, and no other balls, one ball will be removed at random. If the probability is less than 2/5 that the removed ball will be blue, what is the least number of yellow balls that must be in the bag?
a. 17
b. 18
c. 19
d. 20
e. 21
we can have one 77 and (5011) 7s (sevens) OR total 40 numbers
two 77s and (5022) 7s OR total 29 numbers
and so on with the numbers (n) decreasing, it's evident that n=40
IOM C
Tagne wrote: 6. If each term in in the sum a1 + a2 +....+ an is either 7 or 77 and the sum equals 350, which of the following could be n?
a.38
b.39
c.40.
d41.
e.42
My knowledge frontiers came to evolve the GMATPill's methods  the credited study means to boost the Verbal competence. I really like their videos, especially for RC, CR and SC. You do check their study methods at https://www.gmatpill.com

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Q5. P(blue) < 2/5
12 / (12+y) < 2/5
or y > 18
hence minimum number of yellow balls for the probability of a blue ball to be drawn at random of less han 2/5 = 19
hence C
12 / (12+y) < 2/5
or y > 18
hence minimum number of yellow balls for the probability of a blue ball to be drawn at random of less han 2/5 = 19
hence C
 saurabh_maths
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Night reader ,
for Q2 :
2. If n is a multiple of 5 and n = p^2q, where p and q are prime numbers, which of the following will be a multiple of 25?
a. P^2
b. Q^2
c. Pq
d. P^2q^2
e. P^3q
I think ans shd be D.
basically it means n/5 is an integer...
so p^2q is a multiple of 5. i.e atleast one of p or q is 5.
now in order to p^2q divisible by 25 ...look at cases :
p = 5 , q =2 (5 is prime and 2 is also prime)
or
P = 2 , q =5
in either case p^2q^2 will satisfy the condition.
option A will fail if we have p =2 and q = 5.
hence IMO it shd be D.
for Q2 :
2. If n is a multiple of 5 and n = p^2q, where p and q are prime numbers, which of the following will be a multiple of 25?
a. P^2
b. Q^2
c. Pq
d. P^2q^2
e. P^3q
I think ans shd be D.
basically it means n/5 is an integer...
so p^2q is a multiple of 5. i.e atleast one of p or q is 5.
now in order to p^2q divisible by 25 ...look at cases :
p = 5 , q =2 (5 is prime and 2 is also prime)
or
P = 2 , q =5
in either case p^2q^2 will satisfy the condition.
option A will fail if we have p =2 and q = 5.
hence IMO it shd be D.