GMAT Maths (Quantitative) Questions

[GoGMAT Team]

Greetings!

We are starting the thread totally dedicated to math problems and questions you have while preparing for GMAT.

Let's solve several problems at first.

Data Sufficiency

What is the remainder when the positive integer g is divided by 7?
1. When g is divided by 14, the remainder is 8
2. g is the sum of two distinct positive integers

(A) Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
(B) Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.
(C) BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
(D) EACH statement ALONE is sufficient.
(E) Statements (1) and (2) TOGETHER are NOT sufficient.

Problem Solving

If (3^k)*(75^13 )=5*(15^25 ),then k=

(A) 12
(B) 25/13
(C) 17
(D) 25
(E) 13

Post your answers, solutions and thoughts!

[aanshuc]

for DS
from the 1st statement we find the number given to us is of the form 14n+8
therefore we can find its remainder by 7 clearly 1
2nd statement doesnt help us anywhere
remainders will change wid (1+2,2+3) any 2 distinct positive integers
for the PS
we have to equate the powers of the numbers on both sides of the equation
so we check with 5
k comes out to be 12

[ajit.petro]

for DS

1st statement we find the number given to us is of the form 14n+8
therefore we can find its remainder by 7 clearly 1

2nd statement doesnt help us anywhere
remainders will change wid (1+2,2+3) any 2 distinct positive integers

for the PS

k comes out to be 12

[GoGMAT Team]

aanshuc, ajit.petro,

You are absolutely right! You demonstrate sound mathematical logic.

If you are ready for the next round of questions we will post them soon! Stay tuned!

[avrgmat]

Hi,

Do we have the next set of questions?

[GoGMAT Team]

The next set of questions will be published just in a few days! Stay tuned!
If you would like to target any specific areas just let us know.

[GoGMAT Team]

Greetings!

2 more questions for practice! We are open for discussions and explanations!

Problem Solving

To pass a certain test, the ratio of the number of mistakes to the number of questions in the test must be lower than 7:40. If the test has 100 questions, what is the maximum number of mistakes Jack can make so that he can still pass the test?

A 15
B 16
C 17
D 18
E 19

Data Sufficiency

Each large box of chocolates contains 30 chocolates and each small box of chocolates contains 25 chocolates. Did Adam purchase more large boxes of chocolates than small boxes?

(1) The total number of chocolates purchased by Adam was 260.
(2) The mean number of chocolates in the boxes of chocolates purchased by Adam was 26.

(A) Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
(B) Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.
(C) BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
(D) EACH statement ALONE is sufficient.
(E) Statements (1) and (2) TOGETHER are NOT sufficient.

[avrgmat]

This might be a relatively long post.

1. Problem Solving Question --:

a. Approach 1 : Plugging in of the answer choices in the format eg:--

Permissible mistakes are less than (7/40) i.e. .175

Start with any answer choice. I normally start with C.
Total mistakes = 17 (option C) Total Questions = 100.
Ratio = (17/100) = 0.17 i.e. less than permissible and the maximum possible because 18 will be .18 i.e. >.175 and 16 is 0.16 but is also less than .17.

Therefore answer is C.

b. Approach 2 : Making the ratio equal to the asked ratio of x/100.

7/40 translates (7+7+3.5)/40+40+20) i.e. (17.5/100). Answer choice C is the maximum possible answer. Hence answer is C. I preferred using this approach 2 for this question since the ratio was easily convertible. Took me 1:26 seconds.

2. Data Sufficiency --:

This one was a testing one personally. Not sure if I have been able to nail this one. Also took me relatively longer than 2 mins to solve this one.

(i) Total number of chocolates are 260.
This can be split as either -->
200 + 60 i.e. 8 Small and 2 Large or 210 + 50 i.e. 7 Large and 2 Small. Not sufficient.

(ii) We have been given the average/box. Hence the total chocolates from the 2 boxes divided but total boxes is =26.

Approach 1 :
Total chocs = 30L+25S where
L = no. of large boxes and S = no. of small boxes.
Total boxes = L+S

(30L+25S)/(L+S) = 26

On simplifying, 4L=1S i.e. L = (1/4) of S.

Hence number of Large boxes is less than number of Small Boxes.

(ii) is sufficient.

Approach 2 :

No. of Large boxes No. of Small boxes Average

1 (tot=30) 1 (tot=25) (55/2) = 27.5

2 (tot=60) 1 (tot=25) (85/3) = 28.3

1 (tot=30) 2 (tot=50) (80/3) = 26.3

As seen above, as number of smaller boxes increases the average tends to go towards 26.

Eventually,
1 (tot=30) 4 (tot=100) (130/5) = 26
Hence number of small boxes is more. (ii) is sufficient.

Answer is B.

I followed approach 1 for statement (ii) mentioned above and it took me around 3.5 mins for this entire question. I would be interested in understanding a smarter and much faster way to reach answer choice B.

[GoGMAT Team]

Hi avrgmat,
thank you for your quick reply!

Hi everyone,
Do you have any other ideas on the GMAT questions above?
We are striving for them!:)

[avrgmat]

Hi GoGMAT team,

I missed your question on whether specific topics would be of interest. personally, DS questions involving topics of Permutations & Combinations/Statistics would be a great example. Also for the Problem solving, some tweaked examples on topics of "combined work" and "speed-distance" would be great.