GMAT Club Forum - Forums > Problem Solving (PS)

On a certain plane, 2/5 of the passengers speak Farsi and 3/4 speak Hebrew. If all of the passengers on the plane speak at least one of these languages, what is the smallest number of passengers that could be on the plane?

A. 12
B. 15
C. 20
D. 24
E. 40

Which of the following numbers has a zero in its units digit?

I. (4!)×(4!)×(3!)×(11)×(17)×(31)
II. (2!)×(3!)×(3!)×(5)×(17)×(31)
III. (2!)^5×(3!)^5×(4!)^5

A. I only
B. II only
C. III only
D. I, II and III
E. II and III

Set n is a finite set of integers. Are there any even numbers included in set n?

(1) The sum of all the integers in set n is even.
(2) The product of all the integers in set n is even.

What is the greatest value of positive integer x such that 2^x is a factor of 100^80?

A. 40
B. 80
C. 100
D. 160
E. 240

Which of the following is a non-repeating and non-terminating decimal?

A. 1/3
B. 1/4
C. 1/3.5
D. \(\sqrt{\frac{1}{3}}\)
E. \(\sqrt{\frac{1}{4}}\)

Is the positive integer x a perfect square?

(1) x = t^n, where t is a positive integer and n is odd.
(2) x^0.5=k, where k is a positive integer.

If n! and (n + 1)! have the same units digit, then n can be which of the following?

I. n = 10
II. n = 1
III. n = 0

A. I only
B. II only
C. III only
D. I and III
E. I, II, and III

Answer is B.
With just A, we know that the product of the two numbers will be a 4! = 24 X b. Can't make a comment on the unit's place digit with just this information.
With B, we know that the product of the two numbers will be a X 7! = a X 5040. In this case, the unit's digit will always be 0.

Forget conventional ways of solving math questions. In DS, Variable approach is the easiest and quickest way to find the answer without actually solving the problem. Remember equal number of variables and independent equations ensures a solution.

A larger playground has a rectangular-shaped track shaded shown as above figure such that the track has a uniform d as its width, what is the track’s area?

1) The perimeter of smaller playground is 18d.
2) The perimeter of smaller playground is 360.

Attachment:

VeritasPrepKarishma wrote:

prashantbacchewar wrote:

Solution A is 20% salt and Solution B is 80% salt. If you have 30 ounces of solution A and 60 ounces of solution B, in what ratio could you mix Solution A with Solution B to produce 50 ounces of a 50% salt solution?
6:4
6:14
4:4
4:6
3:7

What is faster way to solve this

Forget the volumes for the time being.
You have to mix 20% and 80% solutions to get 50%. This is very straight forward since 50 is int he middle of 20 and 80 so we need both solutions in equal quantities. If this
...

Forget conventional ways of solving math questions. In DS, Variable approach is the easiest and quickest way to find the answer without actually solving the problem. Remember equal number of variables and independent equations ensures a solution.

John wants to put the 78 pencils in the 6 boxes. The number of the each pencil in the boxes is different one another and there is no empty boxes. The second largest box of the number of the pencils is named to be B, is the pencil's number of the box B
...

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There is a sequence An for a positive integer n such that when An-2 is divided by An-1 the remainder is An. If A3=6, A4=0, which of the following can be the value of A1?

A. 48
B. 50
C. 52
D. 56
E. 58

==> If n=4, A2=A3Q+A4=6Q+0=6Q is derived.
If n=3, from A1=A2P+A3=6QP+6=6(QP+1), it becomes always a multiple of 6.
Thus, the answer is A.

Step1 x=100, y=3
Step2 x<y? Yes -> step5, no -> step3
Step3 x -> x/2
Step4 -> step2
Step5 write down x
Step6 finish

If you end at Step6, how many Step2 are passed through?

A. three
B. four
C. five
D. six
E. seven

* A solution will be posted in two days.

(n + 4)! > (n + 2)! > (n - 1)! --> GCD of the 3 numbers = (n - 1)!

(n - 1)! = 5!
n = 6

Answer: C

sabxu1 wrote:

Bunuel wrote:

SOLUTION

\(\frac{31}{125} =\)

(A) 0.248
(B) 0.252
(C) 0.284
(D) 0.312
(E) 0.320

\(\frac{31}{125} =\frac{31*8}{125*8} =\frac{248}{1000} =0.248\).

Answer: A.

why do you choose to times by 8?

s are all in the decimal forms, we need to divide the numerator by denominator.
If we have a calculator, we can directly divide it. But since we are not allowed a calculator, we need to make our lives simpler.

Hence we try to bring denominator in a form by which the division becomes easier.
125 = 5^3
If we multiply 5^3 by 2^3,
...

Flexxice wrote:

Thank you! I tried it in another way and I do not get why I got another answer than you did.

4^17 - 2^28 = 4^17 - 4^14 = 4^3 = 2^6

Because of that, I chose answer A.

We cannot simply subtract the terms.

4^17 - 4^14 = 4^14 (4^3 - 1) = 4^14*(64 - 1) = 4^14 * 63
Here we have taken 4^14 common from both the terms and written the remainder inside the brackets.

Bunuel wrote:

What is the units digit of 26! + 50! + 4! + 4!?

A. 8
B. 6
C. 4
D. 2
E. 0

Let us first write down the factorials of different numbers:

1! = 1
2! = 2
3! = 6
4! = 24
5! = 120
6! = 720

and so on.

If we notice here, all the numbers after 4! will end with a 0.
Here is why:

If we multiply any number by 10, a 0 is added to that number
And a 10 is formed by a 5 and a 2, 10 = 5*2
Till 4!, we do not have a "5" in multiplication. But after that, we will have atleast one
...

USe the theory here => Q*Di+R = Dividend
Smash that D

Arranging the prime factors we can see that 7 is left out as its power is one.
Smash D

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