GMAT Question of the day

How many positive integers less than 10,000 are such that the product of their digits is 210?
(A) 24
(B) 30
(C) 48
(D) 54
(E) 72

210 = 2*3*5*7.

So the numbers have to be made of above four digits.

If we take all 4 primes as separate digits, then 4*3*2*1 = 24 different numbers.

We can also make numbers from the digits 6 (2*3), 5 and 7 = 3*2*1 = 6 different numbers so total 30 numbers.

Hence the answer is B

GMAT question of the day

2304 blocks are to be arranged in heaps in such a way that the number of
blocks in each heap should be equal to the number of heaps. If the number
of blocks in each heap is increased by 16, what will be the number of heaps?

(a) 32
(b) 48
(c) 36
(d) 34

Since the number of blocks in each heap should be equal to the number of heaps

X^2=2304

so X=48

When the number of blocks in each heap is increased by 16.

2304/64 = 36

Hence the number of heaps is 36 .Answer is C

GMAT question of the day

The number of positive integers not greater than 100, which are not divisible
by 2, 3 or 5 is

(a) 24
(b) 26
(c) 29
(d) None of these

We can find the numbers that are divisble by 2,3 and 5 then we can subtract from total numbers to get the numbers that are not divisible.

No. divisible by 2 ---50

No. divisible by 5 ---20

This includes 10 numbers divisible by 2,hence we need to subtract them as they already included.

No. divisible by 3 ---33

This includes 13 numbers divisible by 2 and 6 numbers divisible by 5,hence we need to subtract them as they already included.

Then the total Nos. = 50+10+14 = 74

No. not divisible by 2, 3 or 5 is 100 – 74 = 26

GMAT Question of the Day

If a carton containing a dozen mirrors is dropped, which of the following
cannot be the ratio of broken mirrors to unbroken mirrors?

(a) 2: 1
(b) 3: 1
(c) 3: 2
(d) 7 : 5

Since the total number of mirrors is mentioned as 12 (Dozen) it has to be completely divisible by the ratio.

Example : 7+5=12 , 3+1=4 ,2+1=3 but not 3+2=5.

Hence the solution is D.

GMAT Question of the day

What is the Number of pairs which have 16 as their H.C.F. and 136 as their
L.C.M.?
(a) Only one such pair exists
(b) Only two such pairs exist
(c) More than two pairs exist
(d) No such pairs exist

This is a tricky question and I will post the answer in my next post

Question of the day

If P represents the product of the first 15 positive integers, then P is not a multiple of

a) 99
b) 84
c) 72
d) 65
e) 57


The answers can be expressed in simpler terms as follows
a) 99 = 9 * 11
b) 84 = 7 * 12
c) 72 = 8 * 9
d) 65 = 5 * 13
e) 57 = 3 * 19
The question is to find the number which is not a factor of P.
so the option e is the one with multiple having number other than (1-15) ie, 19.

GMAT question of the day

A heap of pebbles can be made up exactly into groups of 25,,but when made up into groups of 18,27,32,there is in each case a remainder of 11
what is the least number of pebbles that heap contains ?

1)100
2)875
3)864
4)760




LCM of 18,27,32 is 864 and LCM would be exactly divisible by all 3.
So to get a reminder of 11 we need to add 11 to 864 = 875
which is also divisible by 25

PREP FOR GMAT: LEAST COMMON MULTIPLE (L.C.M.)

A common multiple is a number that is a multiple of two or more numbers. The common multiples of 3 and 4 are 0, 12, 24…
The least common multiple (LCM) of two numbers is the smallest number (not zero) that is a multiple of both.

NOTE :
The HCF and LCM of two nos is given. It is possible to find out the two nos uniquely if

Either the sum or the difference between the two nos is known.

We know HCF X LCM = Product of the nos
Given that A-B or A+B is known.
Thus we have 2 equations and two variables, thus the soln can be uniquely determined.

or LCM/HCF = prime no is known.

Then one of the nos = LCM and the other = HCF.

Two numbers are said to be co primes if their HCF is one.

PREP FOR GMAT: HIGHEST COMMON FACTOR (H.C.F)

FACTOR:
A factor of a given number is every number that divides the given number.

Example

16 = 2 x 8, so numbers 2 and 8 are factors of 16.
Also 16 = 16 x 1, so 16 and 1 are factors of 16.
Also 16 = 4 x 4 ,so 4 is a factor of 16
The factors of 10 are 1, 2,4, 8, and 16.

NOTE: Number 1 and the number itself are always factors of any number.

COMMON FACTORS:
When two (or more) numbers have the same factor, that factor is called a common factor.

Example

Factors of 12 are 1, 2, 3, 4, 6, 12.
Factors of 18 are 1, 2, 3, 6, 18.
The common factors of 12 and 18 are 1, 2, 3 and 6.

HIGHEST COMMON FACTOR:
The Highest Common Factor (H.C.F) of two (or more) numbers is the largest number that divides both the numbers. It is also known as G.C.D. (Greatest common divisor)
In other words the H.C.F is the Highest common factors.