Competitive Math Group3

If three metallic spheres of radii 6 cm, 8 cm, and 10 cm are melted to form a single sphere, then the diameter of the new sphere is?

1 Mark(s)

$ 24 \ cm $
$ 30 \ cm $
$ 12 \ cm $
$ 15 \ cm $

If the ratio between the areas of two circles is 4:1 then the ratio between their radii will be?

1 Mark(s)

1:2
2:1
1:3
4:1

If one third of one fourth of a number is 15, then three tenths of that number is?

1 Mark(s)

35
36
45
54

How many lbs. of mixed nuts that contain $26\%$ peanuts must Maria add to 8 lbs. of mixed nuts that contain $64 \%$ peanuts to make a mixture with $42 \%$ peanuts?

1 Mark(s)

$ 11 \ lbs. $
$ 18 \ lbs. $
$ 4 \ lbs. $
$ 17 \ lbs. $

$If \ x \ = \ 3t \ and \ y \ = \ \frac{(t \ + \ 1)}{2} \ and \ x \ = \ 2y \ then \ find \ the \ value \ of \ t \ ?$

1 Mark(s)

1
$ \frac{2}{3} $
$ \frac{1}{2} $
$ \frac{1}{4} $

Working alone, Aliyah can dig a 10 ft by 10 ft hole in six hours. One day her friend Eugene helped her and it only took 3.75 hours. How long would it take Eugene to do it alone?

1 Mark(s)

$ 11.14 \ hours $
$ 12.91 \ hours $
$ 11.95 \ hours $
$ 10 \ hours $

A card is drawn from a pack of 52 cards. The card is drawn at random. What is the probability that it is a spade?

1 Mark(s)

$ \frac{3}{4} $
$ \frac{1}{2} $
$ \frac{1}{4} $
$ \frac{3}{5} $

How many lb of copper which costs $ \$ 3 \ per \ lb$ must be added to $ 6 \ per \ lb$ of pure gold which costs $\$ 6 \ per \ lb$ to make 22 carrot gold which costs $\$ 4 \ per \ lb$?

1 Mark(s)

$ 12 \ lbs. $
$ 19 \ lbs. $
$ 8 per\ lbs. $
$ 13 \ lbs. $

How many cubes of 10 cm edge can put in a cubical box of 1 m edge?

1 Mark(s)

10 10
1000 1000
10000 10000
100 100

Competitive Math Group3 - Grades 6-7 : Question 1 of 9