228 



MEMOIRS NATIONAL ACADEMY OF SCIENCES. 



[Vol. XV, 



EXAMINATION 

 Test 2. Arithmetical 



ALPHA 

 Problems 



Fo 



rm 



1 How many arc 40 guns and C guns? .. . Answer ( 



2 If vou save S6 a month for 5 months, how much will you 

 save; Answer ( 



3 If 32 men are divided into squads of 8, how many squads will 



there be? y- ^T" ( 



4 Mike had 11 cigars. He bought 3 more and then smoked 6. 

 How many cigars did he have left? ........ Answer ( 



5 A company advanced 6 miles and retreated 3 miles. How far 

 was it then from its first position? 



4t ) 



Answer ( 



6 How manv hours will it take a truck to go 48 miles at the rate 



of 4 miles' an hour? •■•■.• ■ • :"*■*"• ( 



7 How many pencils can you buy for 40 cents at the rate oi i 

 for 5 cents? Answer I 



8 A regiment marched 40 miles in five days. The first day they 

 marched 9 miles, the second day 6 miles, the third 10 miles, the 

 fourth 9 miles. How many miles did they march the last 

 , r? . Answer ( 



9 ifyou buy 2 packages of tobacco at 8 cents each andapipe for 

 '55 cents, "how much change should you get from a two-dollar * 



i.ji|? . Answer I J . y.M J 



10 'Ifittakes8men2daystodigal60-footdrain,howmanymen 



are needed to dig it in half a day? Answer ( 



) 



33- > 



11 A dealer bought some mules for S900. He sold them for 81,000, 



-making $25 on each mule How many mules were there?. Answer ( 

 J2 A rectangular bin holds 000 cubic feet of lime. If the bin is 10 



feet wide and 5 feet deep, how long is it? .... Answer ( 



J3 A recruit spent one-eighth of his spare change for post cards 



13. > 



n recruit spent u,it-.,^,,.„ «• ••-- .1-—- .»- - - ■ , ( 



and four times as much for a box of letter paper, and then had « -■ 

 60 cents left. How much money did he have at first?. Answer !■»» J 

 If 2'a tons of hay cost $20, what will 4! i tons cost? Answer ( wat, ) 

 A ship has provisions to last her crew of 600 men 6 months. u 1/ 



How long would it last S00 men? Answer ( *4 ft™» 



If a train goes 200 yards in 10 seconds, how many feet does it 



go in a fifth of a second? ... -Answer (. | J. ) 



17 A U-boat makes 10 miles an hour under water and 20 miles on 

 the surface. How long will it take to cross a 100-mile channel, 

 if it has to go three-fifths of the way under water? . Answer I 



18 If 214 squads of men are to dig 4,060 yards of trench, how 

 many yards must be dug by each squad? . Answer ( 

 A certain division contains 2,000 artillery, 15.000 infantry, and 

 1 000 cavalry If each branch is expanded proportionately 

 u'ntilthcreareinalll9,S00men,'.iowmaiiywillbeaddcdtothe 



artillcrv" ■ ■■ , ■■ . A "f' er < »-°° > 



A commission house which had already supplied 1,897 barrels 

 of apples to a cantonment delivered the remainder of Its stock 

 to 28 mess halls. Of this remainder each mess haU received 47 

 barrels. What was the total number of barrels supplied' Answer (OJ.10 ) 



16 



19 



211 



II 



r o r m /> 



1 How many arc 50 tents and 8 tents? Answer { ST ) 



2 If you save S5 a month for 7 months, how much will you « _ 

 save? - Answer ( *2£ ) 



3 If 40 men are divided into squads of 8, how many squads 



will there be? Answer ( 5 ) 



4 Mike had 12 cigars. He bought 2 more and then smoked 7. 



How many cigars did he have left? Answer ( 7 ) 



5 A company advanced 7 miles and retreated 2 miles. How far 



was it then from its first position? -• Answer ( 5" ) 



6 How many hours will it take a truck to go 65 miles at the rate 



of 5 miles an hour? ' Answer ( 13) 



7 How many pencils can you buy for 30 cents at the lUe of 2 for 



5 cents? Answer ( IX.) 



8 A regiment marched 40 miles in five days. The first day they 

 marched 9 miles, the second day 6 miles, the third 10 miles, 

 the fourth 1 1 miles. How many miles did they march the last 



day? Answer ( H ) 



ft If you buy 2 packages of tobacco at 7 cents each and a pipe 



for 55 cents, how much change Bhould you get from a two- -, 

 dollar bill? ■ Answer ( \.Z\ ) 



10 If it takes 7 men 2 days to dig a 140-foot drain, how many men 



are needed to dig it in half a day? Answer ( 0- » ) 



11 A dealer bought some mules for Si, 000. He sold them for 

 51,200, making $20 on each mule. How many mules were 



there? . . Answer ( \ O ) 



12 A rectangular bin holds 300 cubic feet of lime. If the bin is 10 



feet long and 5 feet wide, how deep is it? Answer ( (* I 



13 A recruit spent one-eighth of his spare change for post cards 



and four times as much for a box of letter paper, and then had a 



30 cents left. How much money did he have at first?. .. .Answer ( .?0 ) 



14 If 4H tons of clover cost $36, what will 2V 2 tons cost?. .Answer ( «&0 > 



15 A ship has provisions to last her crew of 800 men 4 months. . 

 How long would it last 1,200 men? '...Answer (£.1B1m9 



16 If a train goes 150 yards in 10 seconds, how many feet does it 

 go in a fifth of a second? Answer ( 



17 A U-boat goes 10 miles an hour under water and 20 miles an 

 hour on the surface. How long will it take to cross a 100-mile 

 channel if it has to go one-fifth of the way under water? Answer ( 



18 II 341 squads of men are to dig 6,138 yards of trench, how 

 many yards must be dug by each squad? Answer ( 



19 A certain division contains 4,000 artillery, 15,000 infantry, and 

 1,000 cavalry. If each branch is expanded proportionately 

 until there are in all 22,000 men, how many will be added to the 

 artillery? Answer ( 



20 A commission house which had already supplied 1,897 barrels 

 of apples to a cantonment delivered the remainder of its stock 

 to 27 mess halls. Of this remainder each mess hall received 56 

 barrels. What was the total number of barrels supplied? Answer ( 3 *f 0«} ) 



<? ) 



(a ) 



\i > 



tfoo ) 



~orm 



&. 



3-1 



How many are 60 guns and 5 guns? -Answer ( t,5 



If you save S9 a month for 3 months, how much will you 



save? Answer ( 



If 48 men are divided into squads of 8, how many squads will 



there be? Answer ( 



Mike had 11 cigars, He bought 2 more and then smoked 7. 



How many cigars did he have left? Answer ( 



A company advanced 8 miles and retreated 2 miles. How far 



was it then from its first position? .Answer ( 



How many hours will it take a truck to go 42 miles at the rate 



-of 3 miles'an hour? Answer ( 



gHow many pencils can you buy for 60 cents at the rate of 2 



-for 5 cents? Answer ( 



A regiment marched 10 miles in five days. The first day they 

 marched 9 miles, the second day 6 miles, the third 10 miles, the 

 fourth 6 miles. How many miles did they march the last 



day? - ■ Answer ( 



If you buy 2 packages of tobacco at 8 cents each and'a pipe for 

 65*cents,"how much change should you get from a two-dollar ^ 



bill? - .Answer (*|.H ) 



If it takes 4 men 3 days to dig a 120-foot drain, how many men 

 are needed to dig it in half a day? Answer ( 



If ) 



3-4- ) 



s ) 



2.^ ) 



n 



A dealer bought some mules for S2,000. He sold them for 

 $2,400, making $50 on each mule. How many mules were 



there? • ■ Answer ( 



A rectangular bin holds 200 cubic feet of lime. If the bin is 



10 feet long and 5 feet wide, how deep is it? . ... Answer ( 



A recruit spent one-eighth of his spare change for post cards 



and twice as much for a box of letter paper, and then had $1.00 * 



left. How much money did he have at first? Answer (t-^o) 



If 3'^ tons of clover cost S14, what will G 1 $ tons cost?. .Answer (S^.^ ) 

 A ship has pi fi visions to Inst her crew of 700 men 2 months. 



How long would it last 400 men? Answer (3 /Vm^ 



If an aeroplane goes 250 yards in 10 seconds, how many feet 



does it go m a fifth of a second? Answer ( 1 'i ) 



A U-*-oat makes 8 miles an hour under water and 20 miles on 



the surface. How long will it take to cross a 100-mile chan- 



nel, if it has to go two-fifths of the way under water? Answer ( M ) 



If 134 squads of men are to dig 3,618 yards of trench, how 



many yards must be dug by each squad? .Answer ( %.*\ ) 



A certain division contains 5,000 artillery, 15,000 infantry, and 

 1,000 cavalry. If each branch is expanded proportionately 

 until there are in all 23,100 men, how many will be added to the 



artillery'? •< Answer ( Soo ) 



A commission house which had already supplied 1,897 barrels 

 of apples to a cantonment delivered the remainder of its stock 

 to 37 mess halls. Of this remainder each mess hall received 54 

 barrels. What was the total number of barrels supplied?. Answer ftnftS) 



rorm ^?. 



1 How many are 20 boats and 9 boats? - . Answer ( Jfl ) 



2 If you save $4 a month for 9 months, how much will you 



save? Answer ( 3(o ) 



3 If 64 men are divided into squads of 8, how many squads will 



there be' Answer ( *% ) 



4 Mike had 11 cigars. He bought 3 more and then smoked 8. 



How many cigars did he have left? Answer ( t ) 



5 A company advanced 6 miles and retreated 2 miles. How far 



was it then from its first position? Answer ( U. ) 



6 How many hours will it take a truck to go 48 miles at the rate 



of 3 miles an hour? Answer ( 1 (* ) 



7 How many cigars can you buy for $1.00 at the rate of 2 for 



Scents? Answer ( 4-0 ) 



8 A regiment marched 40 miles in five days. The first day they 

 marched 9 miles, the second day 6 miles, the third 10 miles, the 

 fourth 7 miles. How many miles did they march the last 



day? Answer ( Si ) 



9 If you buy 2 packages of tobacco at 7 cents each and a pipe for 



75 cents, how much change should you get from a two-dollar ,. 



bill? Answer(*l.l\ ) 



10 H it takes 5 men 4 days to dig a 200-foot drain, how many men 



are needed to dig it in half a day? Answer ( 1^0 ) 



11 A dealer bought some mules for SI, 200. He sold them for $1,500, 



making $50 on each mule. How many mules were there? . Answer ( ia ) 



12 A rectangular bin holds 500 cubic feet of lime. If the bin is 10 



feet long and 5 feet deep, how wide is it? Answer ( \ o ) 



13 A recruit spent one-eighth of his spare change for post cards 

 and twice as much for a box of letter paper, and then had $2.00 ± 



left. How much money did he have at first? Answer (3.^-0 \ 



14 If hY 2 tons of bark cost $33, what will 3}£ tons cost?. .Answer (*t^_\ ) 

 16 A ship has provisions to last her crew of 400 men 6 months. . 



How long would it last 1,600 men? ; Answer (l/£.™<tt) 



16 If an aeroplane goes 300 yards in 10 seconds; how many feet 



does it go in a fifth of a second? Answer (1*5 ) 



17 A U-boat goes 6 miles an hour under water and 20 miles an 

 hour on the surface. How long will it take to cross a 100-mile 

 channel.if it has to go three-fifths of the way under water?. Answer ( )%. ) 



18 If 214 squads of men are to dig 5,992 yards of trench, how 



many yards must be dug by each squad? Answer ( Jl^i ) 



19 A certain division contains 6,000 artillery, 15,000 infantry, and 

 1,000 cavalry. If each branch is expanded proportionately. 

 untU there are in all 24,200 men, how many will be added to 

 the*artillery? -., Answer ((e OO ) 



30 A commission house which had already supplied 1,897 barrels 

 of apples to a cantonment delivered the remainder of its stock 

 to 38 mess halls. Of this remainder each mess hall received 45 . 

 barrels. What was the total number of barrels supplied?, Aaswer (^WO*\ ) 



Fig. 26.— Group Examination Alpha, Four Forms, Test 2, Arithmetical Problems. 



