Can someone please help me with these questions :
1.
How many odd numbers are there from the integers 700 to 999(inclusive)? If every digit of such an odd number must be non-zero and different.
a. 88
b. 89
c. 90
d. 91
e. 92
----------------------
2. What is the range of (1/101 + 1/102 + 1/103 + ii +1/150)?
a. 0 to 1/2
b. 1/2 to 1/3
c. 1/3 to 2/3
d. 2/3 to 1
e. 1 to 4/3
----------------------
3. If n is an integer from 1 to 96, what is the probability for n*(n+1)*(n+2) being divisible by 8?
a. 25%
b. 50%
c. 62.5%
d. 72.5%
e. 75%
---------------------
4. Data sufficiency:
How many different prime factors does N have?
(1) 2N has 4 different prime factors.
(2) N ^2 has 4 different prime factors.
And how ? Please explain....
Thanks
Sonal
Okay here are the solns
1. Lets first tackle nos starting from 7 and 9
For 7:
a) 1*4*4=16 (Hundreds place occupied by only 7, Tens place by 2,4,6,8, Units place by 1,3,5,9)
b) 1*1*3=3 (Hundreds place occupied by only 7, Tens place by 1, Units place by 3,5,9)
similarly in b the tens place can be occupied by 3, 5, and 9 therefore total nos. in this arrangement= 4*3=12
Therefore total no.s starting from 7= 16+12=28
For 9:
Exactly same logic can be applied for no.s starting from 9 therefore total no.s starting from 7 and 9 = 28*2= 56
For 8:
a) 1*3*5 = 15 (Hundreds place occupied by only 8, Tens place by 2,4,6, Units place by 1,3,5,7,9)
b) 1*1*4=4 (Hundreds place occupied by only 8, Tens place by 1, Units place by 3,5,7,9)
In b in th tens place we can have 3,5,7 and 9 instead of one therefore total possibilitiesin b = 4*5=20
therefore total possibilities for nos starting from 8 = 15+20=35
Hence total odd no.s satisfying the cond = 56+35=91
2. 1/100= 0.01 if we add up 0.01 50 times (since ther are 50 no.s) we get 0.5 =1/2 which is the upper limit of the range
1/150=0.0067 approx so 50 times 0.0067= 1/3 which is the lower limit of the range
Hence the answer is between 1/2 and 1/3
3. Total products = 96 (i.e. 1*2*3, 2*3*4, ........., 96*97*98
The products that will be divisible by 8 will be when n is an even no i.e. 2*3*4, 4*5*6, 6*7*8 and so on , since from 1 to 96 there will be 48 even no.s
the probability that n*n+1*n+2 is divisble by 8 = 48/96=50%
4. I think the answer is e but not sure