Problem Solving Word Problems

[GMAT math practice question] If \(100! = 100 x 99 xx 2 x 1\) can be written as \((2^a)(3^b)(5^c)(7^d)\)., what is \(a\)? A. \(86\) B. \(97\) C. \(108\) D. \(119 \) E. \(131\)
Answer: B
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GMAT QUANT Problem Solving Divisibility / Multiples / Factors
1) If n is the product of the integers from 1 to 20 inclusive, what is the greatest integer k for which 2^k is a factor of n?
A. 10
B. 12
C. 15
D. 18
E. 20
2) What is the remainder when n^2+7 is divided by 8, where n is an odd prime number?
A. 0
B. 2
C. 3
D. 4
E. 6
3)If n is the product of the integers from 1 to 8, inclusive, how many different prime factors greater than 1 does n have?
(A) (...)

GMAT QUANT, QUESTIONS DISTANCE / RATE WORK /RATE MIXTURE PROBLEMS
DISTANCE / RATE
A man can row at a speed of 5 km/hr in still water. If he rows a certain distance upstream and back to the starting point in a river which flows at 1.5 km/hr, what is his average speed for the double journey? A. 3.5 km/h B. 4.55 km/h C. 5 km/h D. 5.5 km/h E. 6.5 km/h
(b)
Seb’s watch gains 5 seconds in every 3 hours, whereas Lewis’ watch loses 10 seconds in every 2 hours. If both watches are (...)

GMAT QUANT Problem Solving level 600, Overlapping Sets
Language - Number of students
Arabic - 18
English - 16
French - 14
The table above shows the number of students at Adam Zachary High School who are proficient in Arabic, English and French. Three students know all these three languages, five students know Arabic and English only, six students know Arabic and French only and four students know English and French only. How many different students are there in the school?
A - 25 (...)

GMAT QUANT Problem Solving level 600, Distance/Rate Problems
Harvey runs a 30-mile course at a constant rate of 4 miles per hour. If Clyde runs the same track at a constant rate and completes the course in 90 fewer minutes, how fast did Clyde run?
A. 4.5 miles per hour
B. 5 miles per hour
C. 5.5 miles per hour
D. 6 miles per hour
E. 7 miles per hour

GMAT QUANT Problem Solving level 600, Remainders
If n is a prime number greater than 3, what is the remainder when n^2 is divided by 12 ?
(A) 0
(B) 1
(C) 2
(D) 3
(E) 5

GMAT QUANT Problem Solving level 600, Fractions/Ratios/Decimals
A certain barrel is 1/5 full. When k liters of liquid are added to the barrel, it becomes 2/3 full. In terms of k, what is the capacity of the barrel, in liters?
A. 3/8*k
B. 7/15*k
C. 15/7*k
D. 7/3*k
E. 8/3*k

GMAT QUANT Problem Solving level 600, Arithmetic
If S is the product of the integers from 1 to 100, inclusive, and T is the product of the integers from 1 to 101, inclusive, what is 1/S+1/T in terms of T ?
A)T/101
B)T/100+100
C)100+T/T
D)102/T
E)T+1/100

GMAT QUANT Problem Solving level 600, Coordinate Geometry, slop
Line J has a y-intercept of 6 and passes through point (a,b). What is the slope of Line J in terms of a and b?
A. (a−6)/b
B. (a−b)/6
C. (6−a)/b
D. (6−b)/a
E. (b−6)/a

GMAT QUANT Problem Solving level 600, Functions And Custom Characters
The operation ⊗ is defined by x⊗y=xexp2/y+x/y for all numbers x and y, where y≠0. What is the value of (9⊗(−9))+((−9)⊗9))?
A. -4
B. -3
C. -2
D. 1
E. 2