Must or Could be True GMAT, GRE Question

If 4<(7-x)/3, which of the following must be true?

I. 5<x
II. |x+3|>2
III. -(x+5) is positive

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

GMAT Remainder Quant Question

How many two-digit whole numbers yield a remainder of 3 when divided by 10 and also yield a remainder of 3 when divided by 4?

A) One
B) Two
C) Three
D) Four
E) Five

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If we arrange every 2 digit number then divide by 10 these numbers would all give us remainder 3. So, the number will have 3 in its unit digit : {13 , 23, 33, 43, 53, 63, 73, 83, and 93}

If we divide each number by 4 to see which of them yields reminder 3 then we should see the first number in the set, (13), yields reminder 1. Cross off.

The second number in the set, ( 23), gives us the remainder 3. Keep it.

the third number in the set gives reminder 1. If we continue this then we would see the pattern will be repeated. The even numbers in the set will give a reminder 3

if we count the even numbers that work {23, 43, 63, and 83} then we have 4 numbers

D.

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GMAT, GRE Powers And Integers Quantitative Question

If 2^5, 3^3, and 13^2 are all factors of the product of 936 and w where w is a positive integer, what is the smallest possible value of w?

A. 26
B. 39
C. 42
D. 65
E. 156

Number Properties GMAT - odds and evens

How many positive even integers less than 100 contain digits 4 or 7?

A. 16
B. 17
C. 18
D. 19
E. 20

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There are 2 one-digit numbers {4 and 7 }. One of them is even. 

For the two-digit numbers (a and b): 

Numbers that have 4 or 7 for the first digit (4b, 7b).
Since even numbers must end by even digit, b could be {0, 2, 4, 6 or 8}. There are 2 × 5 = 10 such numbers.

Numbers that have 4 as the second digit (a4). These are all even.

The first digit, a, can be anything except 0. So there are 1 × 9 = 9 numbers.

Numbers that have 7 as the second digit (a4, b7) and these are all odd.

Note, that we’ve counted twice the two-digit numbers that have 4 as the second digit and 4 or 7 as the first (44, 74).

Therefore we have 1 + 10 + 9–2 = 18 possible variants overall.

C

GMAT Percent and Interest Question

A t-shirt company charges a flat $50 set-up fee plus $4 per shirt and requires 14 days processing time. For a rush job, the company charges an additional $50 rush set-up fee, plus a surcharge of $1 per shirt per day (in addition to the original amount) for each day less than the standard 14-day processing time. (For instance, 13 days notice would be $5 per shirt, 12 days would be $6 per shirt, etc.)

If a customer orders 50 shirts 5 days prior to his desired pickup date, by what percent is his charge greater than it would have been had he provided at least 14 days’ notice?

A. 180%
B. 200%
C. 210%
D. 280%
E. 300%

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The cost of purchasing 50 shirts with at least 14 days notice:

50 + 4(50) = 250

In the case of a 5-day notice — 9 days fewer than 14-day notice — each shirt would then be charged $4 + $9 = $13. Then the $50 rush fee would also be added. 

50 + 50 + 13(50) = 100 + 650 = 750

We can now determine the percent change, using the formula percentage Percent change is [(new — old)/old] x 100 percent.

(750–250)/250 x 100

500/250 x 100 = 2 x 100 = 200 percent

B

GMAT Probability Problem -- Ordering Tallest to Shortest

Eight women of eight different heights are to pose for a photo in two rows of four. Each woman in the second row must stand directly behind a shorter woman in the first row. In addition, all of the women in each row must be arranged in order of increasing height from left to right. Assuming that these restrictions are fully adhered to, in how many different ways can the women pose? 

(A) 2
(B) 14
(C) 15
(D) 16
(E) 18

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There are too many conditions to use a forumla straight away, so let’s work out some options manually. I generally use this approach where a lot of conditions appear in a GMAT question.

Shortest (1) and highest (8) women are fixed:
XXX8
1XXX

2 and 7 have two options, so total 4 patterns:

1:

2xx8
1xx7

|2468| |2568|
|1357| |1347|

2.

2x78
1xxx

|2478| |2578| |2678|
|1356| |1346| |1345|

3.

xxx8
12x7

|4568| |3468| |3568|
|1237| |1257| |1247|

4.

xx78
12xx

|3478| |3678| |3578| |5678| |4578| |4678|
|1256| |1245| |1246| |1234| |1236| |1235| 

14 options.

B